# How to calculate a derivative in Matlab / Octave

To calculate the derivative of a function f (x) in Matlab and Octave use the function diff()

**diff(f,x,n)**

The parameters of the function are

- f is the function
- x is the derivation variable
- n is the degree of derivation

**Note**. The order of derivation is equal to 1 by default (first derivative). The function variables must be defined as symbols. In Octave the diff function requires the installation and loading of the Symbolic library.

## Examples

**Example 1 (first derivative)**

Define a variable as symbols

syms x

Define the function x^{2}

f=x**2

Derive the function with the diff () function and specify the variable for differentiation.

diff(f,x)

The result is the first derivative.

ans = (sym) 2*x

**Example 2 (second derivative)**

To calculate the second derivative of the previous function, specify the order of the derivative equal to 2.

diff(f,x,2)

The output is the second derivative.

ans = (sym) 2

**Example 2 (third derivative)**

To calculate the third derivative of a function, specify the order of the derivative equal to 3.

diff(f,x,3)

The output result is the third derivative.

ans = (sym) 0

**Report us an error or send a suggestion to improve this page**