differentiation matlab

First let us enter the function and plot its graph. Here's my code so far for the function: function [df] = numericalDerivative(x,f,type); n = length(x); The sum and subtraction rules state that if f and g are two functions, f' and g' are their derivatives respectively, then. A = x.^5 + 7*x.^4 - 2*x.^2 By default, the differentiation is done w.r.t the variable identified by ‘symvar’. Explore 1000+ varieties of Mock tests View more. Title : Differentiation in MatlabLearning outcome :0:00 What is Differentiation01:55 Syntax of differentiation04:34 Example10:56 Practise Problems-----. For example, I would like to differentiate y^3*sin(x)+cos(y)*exp(x)=0 with respect to dy/dx.. diff (A, var) can be used to calculate the differentiation of A w.r.t the desired variable, i.e. (b)Numerically differentiate the second derivative of the measured y (x) data . MATLAB helps you take your ideas beyond the desktop. Our input ‘A’ will be differentiated w.r.t this variable ‘t’. The function to derive is 10+15x+20x^2 from 0 to 10 using steps of 0.25. Found inside – Page 101differentiation. and. integration. In this chapter we propose methods for the numerical approximation of derivatives and integrals of functions. In groups of 2, create a MATLAB program to numerically differentiate and integrate the function v=e (cos (t)/ (t+1)) for the range t=0 to 10. Fractional Order Differentiation and Robust Control Design . As we can see in the output, we have obtained differentiation of our input function ‘A’ as 5*x^4 + 28*x^3 – 4*x using ‘diff (A) function’, which is the same as expected by us. author employs MATLAB to reinforce concepts and solve problems that require heavy computation. Numerical Differentiation in Matlab Programming. For example, let us compute the derivative of the function f(t) = 3t2 + 2t-2, Create a script file and type the following code into it −, When the above code is compiled and executed, it produces the following result −, Following is Octave equivalent of the above calculation −, Octave executes the code and returns the following result −. 0. First Derivatives: Finding Local Minima and Maxima, Second Derivatives: Finding Inflection Points, Mathematical Modeling with Symbolic Math Toolbox. Four out of the six patients showed calcifications at computed tomography images and their SWI images demonstrated . MATLAB Code for Numerical differentiation function. Here, use the numeric solver vpasolve to calculate floating-point approximations of the solutions: (0.578718426554417483196010858601961.8651543689917122385037075917613-1.4228127856020972275345064554049-1.8180342567480118987898749770461 i-1.4228127856020972275345064554049+1.8180342567480118987898749770461 i-0.46088831805332057449182335801198+0.47672261854520359440077796751805 i-0.46088831805332057449182335801198-0.47672261854520359440077796751805 i)[vpa('0.57871842655441748319601085860196'); vpa('1.8651543689917122385037075917613'); - vpa('1.4228127856020972275345064554049') - vpa('1.8180342567480118987898749770461i'); - vpa('1.4228127856020972275345064554049') + vpa('1.8180342567480118987898749770461i'); - vpa('0.46088831805332057449182335801198') + vpa('0.47672261854520359440077796751805i'); - vpa('0.46088831805332057449182335801198') - vpa('0.47672261854520359440077796751805i')]. Symbolics can further be used to solve equations that vary with time or with respect to one another. the variable passed as an argument. Please contact Soc . The declaration syms x y(x), on the other hand, forces MATLAB to treat y as dependent on x facilitating implicit differentiation. For example the equation f"(x) + 2f'(x) = 5sin3x should be entered as −. Passing input function ‘A’ to the diff function. 1. What is a symbolic expression (syms) and how do. If we need differentiation w.r.t the variable of our choice, we can use diff (A, var). MATLAB executes the code and returns the following plot −, Here is Octave equivalent code for the above example −. Differentiation. Symbolic expressions can allow for the evaluation of equations as shown in a previous post on symbolics. Found inside – Page 4788.3 Numerical Differentiation As we have seen , the derivative of a function can be interpreted graphically as the slope of the function . Use these syntaxes for sfit objects. Found inside – Page 204... constant function 8-18 frequency convolution 8-15 frequency differentiation 8-13 frequency shifting 8-11 imaginary time functions - Fourier J transform ... Below is the syntax for Differentiation in Matlab: diff (A) diff (A, var) diff (A, n) Explanation: diff (A) will calculate the differentiation of A w.r.t variable provided by symvar (A, 1). Hadoop, Data Science, Statistics & others. Found inside – Page 214x is the point about which the derivative is computed. x is the distance to a neighboring point whose location therefore will be x + x. The expression f has a local maximum at x = 1.286 and a local minimum at x = -0.189. ans = x^2. Found insideDifferentiation of the function f(t) of Example 3.7 using the first-order operational matrix Dg(m) TABLE 3.7 Comparison of Results of Differentiation of the ... For example, let us compute the derivative of the function f (t) = 3t 2 + 2t -2. Creating the polynomial function of degree 4. Share. It returns a symbolic solution with a set of arbitrary constants that MATLAB labels C1, C2, and so on. ALL RIGHTS RESERVED. Let us take up a simple example of a first order differential equation: y' = 5y. We will follow the following 2 steps: Step 1: Create the function of variables ‘x’ and ‘t’, Step 2: Calculate the differentiation using ‘diff (A, var) function’, syms x t Found inside – Page 2-69Often the information we want to extract from the data is embedded in their derivative rather than in the data themselves. On the other hand, ... ans = -s^2*sin (s*t) Note that diff (f, 2) returns the same answer because t is the default variable. Facebook: https://www.facebo. Let us compute the second derivative of the function y = f(x) = x .e-3x, MATLAB executes the code and returns the following result −. Found inside – Page 49515.4 CALCULUS: INTEGRATION AND DIFFERENTIATION MATLAB has functions that perform common calculus operations on a mathematical function f(x), ... The chain rule states that, derivative of the function of a function h(x) = f(g(x)) with respect to x is, When you run the file, MATLAB displays the following result −, The following table provides the derivatives of commonly used exponential, logarithmic and trigonometric functions −. MATLAB provides the dsolve command for solving differential equations symbolically. Explanation: Initializing the variable ‘x’ & ‘t’. MATLAB provides the diff command for computing symbolic derivatives. Along with several updates and changes from the third edition, the text continues to evolve to meet the needs of today s instructors and students. Found inside – Page 218We sought run times roughly equivalent to hand-coding the corresponding derivative calculations in MATLAB itself. For mechanics problems, we also required ... Viewed 770 times 2 2 $\begingroup$ I am trying to implement . I also show you how you can find higher. Follow asked Jun 27 '14 at 18:14. X and Y must be double-precision arrays and the same size and shape as each other. Before creating a symbolic expression, declare symbolic variables: By default, solutions that include imaginary components are included in the results. Be sure to include titles and labels so the plots are easily identifiable. Higher derivatives are indicated by following D by the order of the derivative. The most efficient way to compute second or higher-order derivatives is to use the parameter that specifies the order of the derivative: 18 x+34σ1-2 6 x2-1 9 x2+34 x+6σ12-12 x σ2σ12+2 6 x2-12 σ2σ13where  σ1=2 x3-x+3  σ2=3 x3+17 x2+6 x+1(18*x + 34)/(2*x^3 - x + 3) - (2*(6*x^2 - 1)*(9*x^2 + 34*x + 6))/(2*x^3 - x + 3)^2 - (12*x*(3*x^3 + 17*x^2 + 6*x + 1))/(2*x^3 - x + 3)^2 + (2*(6*x^2 - 1)^2*(3*x^3 + 17*x^2 + 6*x + 1))/(2*x^3 - x + 3)^3, 2 68 x6+90 x5+18 x4-699 x3-249 x2+63 x+1722 x3-x+33(2*(68*x^6 + 90*x^5 + 18*x^4 - 699*x^3 - 249*x^2 + 63*x + 172))/(2*x^3 - x + 3)^3. Open Live Script. Many new features are added continuously since the development and additions are made in close cooperation with the user base. As we can see in the output, we have obtained differentiation of our input function ‘A’ as 2*t*x*cos (t^2*x) + 3*t^2*x*sin (t^3*x) using ‘diff (A, var) function’, which is same as expected by us. Implicit differentiation Given the simple declaration syms x y the command diff(y,x) will return 0. This method is better compare to Simple Euler method. An introduction to both automatic differentiation and object-oriented programming can enrich a numerical analysis course that typically incorporates numerical differentiation and basic MATLAB computation. Answered: Konstantin Ninidze on 24 Apr 2021. Unlike a purely symbolic approach, automatic differentiation evaluates expressions numerically early in the computations, rather . Here, consider only real values of x by setting the assumption that x is real: As an example, create a rational expression (i.e., a fraction where the numerator and denominator are polynomial expressions). Implements a bicomplex class in MATLAB, which can be used for bicomplex differentiation. The MATLAB function 'diff' is used for performing symbolic differentiation and the function format is as follows. Symbolics can further be used to solve equations that vary with time or with respect to one another. Found inside – Page 52You can use diff to differentiate symbolic expressions, and also to approximate the derivative of a function given numerically (say by an M-file): >> syms x ... ans = -s^2*sin (s*t) Note that diff (f, 2) returns the same answer because t is the default variable. Right now I am looking for a way to do implicit differentiation in matlab. Approximate the exact solution numerically by using the double function: Now find the local minimum and maximum of f. If a point is a local extremum (either minimum or maximum), the first derivative of the expression at that point is equal to zero. The formula of Euler method is At here, we solve the differential equation by using Euler method with the help of MATLAB. This will give us the 3rd derivative of our input function. Web browsers do not support MATLAB commands. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. Found inside – Page 1825 Numerical Differentiation Given the function f ( x ) , compute d " f / dx " at given x 5.1 Introduction Numerical differentiation deals with the following ... For example, the first derivative of sin (x) with respect to x is cos (x), and the second derivative with respect to x is -sin (x). Example 3. Found inside – Page 183Automatic Differentiation Interestingly, there is yet another approach that offers us the best of both worlds. It is the Automatic Differentiation approach. For this purpose, we will write f'(x) for a first order derivative and f"(x) for a second order derivative. "This book is designed to serve as a core text for courses in advanced engineering Chebyshev spectral differentiation matrix for mapped domain. In other words stationary points are where f'(x) = 0. Open Live Script. The classical finite-difference approximations for numerical differentiation are ill-conditioned. Found inside – Page 97... is symbolically given, the analytical solutions to the differentiation problem can be obtained directly with the MATLAB built-in function diff(). The basic unit in the MATLAB programming language is the matrix, and this makes MATLAB the ideal tool for working with differentiation matrices. MATLAB provides an int command for calculating integral of an expression. Viewed 1k times 1 1. 1998]. Let us briefly state various equations or rules for differentiation of functions and verify these rules. ans = -s^2*sin (s*t) Note that diff (f, 2) returns the same answer because t is the default variable. Please note that we have passed ‘t’ as 2nd argument. Mathematically, the differentiation of sin (x*t^2) – cos (x*t^3) w.r.t ‘t’ is 2*t*x*cos (t^2*x) + 3*t^2*x*sin (t^3*x). Les navigateurs web ne supportent pas les commandes MATLAB. Differentiate Polynomial. Differentiation and Integration in Matlab. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS. MATLAB provides us the ability to perform numerous mathematical operations, In this topic, we are going to learn about MATLAB Derivative. Numerical derivative - diff (y)./diff (x) will give the slope of each interval for the lists of x and y values. Found inside – Page 41The symbolic equation uses the letter D to denote differentiation with respect to the independent variable. D followed by a digit denotes repeated ... This toolbox implements automatic/algorithmic differentiation for matlab using sparse representation for jacobians. Ask Question Asked 5 years, 9 months ago. ️SUBSCRIBE https://bit.ly/drmanabIn this video, we will learn how to perform Numerical differentiation of discrete experimental data in matlab and and sa. Fractional Order Differentiation and Robust Control Design : CRONE, H-infinity and Motion Control.. diff (A, n) can be used to get the ‘nth’ derivative of the function. 33 4 4 bronze badges How does MATLAB Derivative work? That is, by default, x and y are treated as independent variables. Do you want to open this example with your edits? Active 4 years, 5 months ago. When you run the file, it displays the following result −. ans = -s^2*sin (s*t) Note that diff (f, 2) returns the same answer because t is the default variable. For a function y = f(x) the points on the graph where the graph has zero slope are called stationary points. Numerical integration functions can approximate the value of an integral whether or not the functional expression is known: When you know how to evaluate the function, you can use integral to calculate integrals with specified bounds. Found inside – Page 199Differentiation of a Fourier series In certain instances we only have the Fourier series representation of a function f ( t ) . Can we find the derivative ... Obtain the function values at these points using subs: (3 σ2-17 σ5-σ6+15682-σ4+σ1+1134σ6+2 σ2-σ5-21968-σ4+17 σ6+σ5-15682+3 σ3+σ1-1134σ6-2 σ3+σ5-21968)where  σ1=σ7σ91/6 σ81/4  σ2=σ5-σ6+15683  σ3=σ6+σ5-15683  σ4=σ8σ91/6  σ5=σ76 σ91/6 σ81/4  σ6=σ86 σ91/6  σ7=337491 6 3 3 1789396323559826+2198209982639304+2841 σ91/3 σ8578-9 σ92/3 σ8-361 σ8289  σ8=2841 σ91/31156+9 σ92/3+361289  σ9=3 178939632355176868+2198209530604[(3*(sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) - sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)) + sym(15/68))^sym(3) - 17*(sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) - sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)) + sym(15/68))^sym(2) - sqrt(((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6) + sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) + sym(11/34))/(sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)) + 2*(sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) - sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)) + sym(15/68))^sym(3) - sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) - sym(219/68)); -(sqrt(((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6) + 17*(sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)) + sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) - sym(15/68))^sym(2) + 3*(sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)) + sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) - sym(15/68))^sym(3) + sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) - sym(11/34))/(sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)) - 2*(sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)) + sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) - sym(15/68))^sym(3) + sqrt((337491*sqrt(sym(6))*sqrt((3*sqrt(sym(3))*sqrt(sym('178939632355')))/9826 + sym('2198209/9826')))/39304 + (2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/578 - 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3)*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)) - (361*sqrt((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289)))/289)/(6*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/6)*((2841*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(1/3))/1156 + 9*((sqrt(sym(3))*sqrt(sym('178939632355')))/176868 + sym('2198209/530604'))^sym(2/3) + sym(361/289))^sym(1/4)) - sym(219/68))].
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