Differential or Derivatives in MATLAB (original) (raw)

Last Updated : 23 Aug, 2021

Differentiation of a function y = f(x) tells us how the value of y changes with respect to change in x. It can also be termed as the slope of a function.

Derivative of a function f(x) wrt to x is represented as {\displaystyle f'(x)= \frac {dy}{dx}}

MATLAB allows users to calculate the derivative of a function using diff() method. Different syntax of diff() method are:

• f' = diff(f)
• f' = diff(f, a)
• f' = diff(f, b, 2)

f' = diff(f)

It returns the derivative of function f(x) wrt variable x.

Example 1:

Matlab `

% Create a symbolic expression in variable x syms x f = cos(x); disp("f(x) :"); disp(f);

% Derivative of f(x) d = diff(f); disp("Derivative of f(x) :"); disp(d);

`

Output :

Example 2: Evaluating the derivative of a function at a specified value using subs(y,x,k).

• subs(y,x,k), it gives the value of function y at x = k. Matlab `

% Create a symbolic expression in

variable x

syms x f = cos(x); disp("f(x) :"); disp(f);

% Derivative of f(x) d = diff(f); val = subs(d,x,pi/2);

disp("Value of f'(x) at x = pi/2:"); disp(val);

`

Output :

f' = diff(f, a)

• It returns the derivative of function f with respect to variable a. Matlab `

% Create a symbolic expression in variable x syms x t; f = sin(x*t); disp("f(x) :"); disp(f);

% Derivative of f(x,t) wrt t d = diff(f,t); disp("Derivative of f(x,t) wrt t:"); disp(d);

`

Output :

f' = diff(f, b, 2)

It returns the double derivative of function f with respect to variable b.

Example 1:

Matlab `

% Create a symbolic expression in % variable x,n syms x n; f = x^n; disp("f(x,n) :"); disp(f);

% Double Derivative of f(x,n) wrt x d = diff(f,x,2); disp("Double Derivative of f(x,n) wrt x:"); disp(d);

`

Output :

In the same way, you can also calculate the k-order derivative of function f using diff(f,x,k).

Example 2:

Calculating the partial derivative {\displaystyle {\frac {\partial (f,g)}{\partial (u,v)}}} } using Jacobian matrix and determinant.

• {\frac {\partial (f,g)}{\partial (u,v)}} = {\displaystyle {\begin{aligned}{\begin{vmatrix}{\frac {\partial (f)}{\partial (u)}}&{\frac {\partial (f)}{\partial (v)}}\\\\{\frac {\partial (g)}{\partial (u)}}&{\frac {\partial (g)}{\partial (v)}}\end{vmatrix}}\end{aligned}}} Matlab `

% Create a symbolic expression in variable % u and v syms u v; f = u^2; g = sin(v)(3u); disp("f(u,v) :"); disp(f); disp("g(u,v) :"); disp(g);

% Jacobian matrix of function f(u,v) and % g(u,v) J = jacobian([f; g], [u v]); disp("Jacobian matrix :"); disp(J);

% Determinant of Jacobian matrix d = det(J); disp("Determinant of Jacobian matrix:"); disp(d);

`

Output :