MATLAB 2012 PARTIAL DERIVATIVE VERIFICATION
MATLAB 2012 PARTIAL DERIVATIVE CODE

Y = 3*Sin(x)+7*Cos(5*x) % defining the function When you run the file, it displays the following result в€’ Lhs = diff(y,2)+y %evaluting the lhs of the equationДisp('No, the equation does not hold true') Y = 3*sin(x)+7*cos(5*x) % defining the function We will have to find out whether the equation f' + f = -5cos(2x) holds true. Given that a function y = f(x) = 3 sin(x) + 7 cos(5x).

MATLAB 2012 PARTIAL DERIVATIVE CODE

MATLAB executes the code and returns the following result в€’ Let us compute the second derivative of the function y = f(x) = x. To compute higher derivatives of a function f, we use the syntax diff(f,n).

% symbolic packages does not have this support

The following table provides the derivatives of commonly used exponential, logarithmic and trigonometric functions в€’ Function When you run the file, MATLAB displays the following result в€’ The chain rule states that, derivative of the function of a function h(x) = f(g(x)) with respect to x is, x (n-1)ДЄ direct outcome of this rule is that the derivative of any constant is zero, i.e., if y = k, any constant, then The polynomial or elementary power rule states that, if y = f(x) = x n, then f' = n. The quotient rule states that if f and g are two functions, f' and g' are their derivatives respectively, then, The product rule states that if f and g are two functions, f' and g' are their derivatives respectively, then, The sum and subtraction rules state that if f and g are two functions, f' and g' are their derivatives respectively, then, H(x) = af(x) + bg(x) with respect to x is given by в€’ For this purpose, we will write f'(x) for a first order derivative and f'(x) for a second order derivative.ДЇollowing are the rules for differentiation в€’ Rule 1ДЇor any functions f and g and any real numbers a and b are the derivative of the function в€’

Let us briefly state various equations or rules for differentiation of functions and verify these rules.

MATLAB 2012 PARTIAL DERIVATIVE VERIFICATION

Verification of Elementary Rules of Differentiation Octave executes the code and returns the following result в€’ When the above code is compiled and executed, it produces the following result в€’ДЇollowing is Octave equivalent of the above calculation в€’ In its simplest form, you pass the function you want to differentiate to diff command as an argument.ДЇor example, let us compute the derivative of the function f(t) = 3t 2 + 2t -2 ExampleД¬reate a script file and type the following code into it в€’ MATLAB provides the diff command for computing symbolic derivatives.

Matlab 2012 partial derivative