Calculating Derivatives in Matlab/Octave

To compute the derivative of a function f(x) in Matlab or Octave, utilize the diff() function:

diff(f,x,n)

Parameters of the diff() function are as follows:

• 'f' : the function to be differentiated.
• 'x' : the variable with respect to which differentiation is performed.
• 'n' : the order of differentiation.

Note. By default, the order of differentiation is set to 1, implying the first derivative. Ensure that the function variables are defined as symbols. In Octave, the `diff` function necessitates the installation and activation of the Symbolic library.

Examples

Example 1 (First Derivative)

Define a variable as a symbol:

syms x

Define the function f = x²

f=x**2

Differentiate the function using the diff() function, specifying the differentiation variable:

diff(f,x)

The result represents the first derivative:

ans = (sym) 2*x

Example 2 (Second Derivative)

To compute the second derivative of the aforementioned function, set the order of differentiation to 2:

diff(f,x,2)

The output represents the second derivative:

ans = (sym) 2

Example 2 (Third Derivative)

For the third derivative of the function, set the order of differentiation to 3:

diff(f,x,3)

The resulting output is the third derivative:

ans = (sym) 0