Categories

# MATLAB Derivative

MATLAB is a programming environment that is interactive and is used in scientific computing. It is extensively used in a lot of technical fields where problem-solving, data analysis, algorithm development, and experimentation is required. The discipline-specific software is extensively written using MATLAB. MATLAB provides us the ability to perform numerous mathematical operations, In this topic, we are going to learn about MATLAB Derivative.

## How does MATLAB Derivative work?

Differentiation is a calculus tool that calculates small changes in a function. Differentiation or derivative is the rate of change of a function w.r.t. some variable. It calculates how sensitive our output is concerning any change in our input.

Mathematically, it can be represented as f(x)/dx, where dx represents the change in the value of function f (x), concerning the variable x.

Let us now understand how derivative works in MATLAB.

## Syntax of derivative:

• diff (f)
• diff (f, n)
• diff (f, var)
• diff (f, var, n)

## Examples of MATLAB Derivative

Here are the following examples mention below

## Example 1 – diff (f):

This function will differentiate ‘f’ with the variable x

Here is an example where we compute the differentiation of a function using diff (f):

Lets us take a polynomial function defined as:

``x ^ 4 + 3 x ^ 3 + 4 x ^ 2 + 5 x + 1``

### Syntax

``df = diff (f, x)``

The function diff will return derivative value of the functionx ^ 4 + 3 x ^ 3 + 4 x ^ 2 + 5 x + 1:

``4x^3 + 9x^2 + 8x + 5``

## Input:

``````syms f(x)
f(x) = x ^ 4 + 3*x ^ 3 + 4*x ^ 2 + 5*x + 1
df = diff (f, x)``````

## Example 2 – diff (f, n):

This function is used to calculate the nth derivative of the input function. ‘n’ here is passed as an argument.

Here is an example where we compute ‘nth’ derivative of a function using diff (f, n):

Lets us take another polynomial function defined as:

``3 x ^ 3 + 2 x ^ 2 + 7 x + 5``

For our example, we will calculate the 2nd derivative.

Mathematically, our output should be:

``18x + 4``

## Input:

``````syms f(x)
f(x) = 3*x^3 + 2*x^2 + 7*x + 5
df = diff (f, 2)``````

## Output:

As we can see, diff (f, n) has calculated the 2nd derivative of our input function.

## Example 3 – diff (f, var):

This function will find the derivative of ‘f’ w.r.t the variable in the argument.

Here is an example where we compute differentiation of a function using diff (f, var):

Lets us take a sine function defined as:

``Sin(x*t^2)``

For our example, we will calculate the derivative w.r.t ‘t’

Mathematically, our output should be:

``2txcos(t^2x)``

## Input:

``````syms x t
diff(sin(x*t^2),t)``````

## Output:

As we can see, the derivative is calculated w.r.t.  ‘t’ as expected by us.[Notice that we have passed ‘t’ as an argument. Diff function will now take the derivative w.r.t ‘t’]

## Example 4 – diff (f, var, n):

This function will calculate the ‘nth’ derivative of the input function w.r.t the variable we pass as an argument.

Below is the example where we calculate the derivative of a function using diff (f, var, n):

Lets us take a sine function defined as:

``Sin(x*t^4)``

For our example, we will calculate the ‘2nd’ derivative w.r.t ‘t’

Mathematically, our output should be:

``12t^2xcos(t^4x) - 16t^6x^2sin(t^4x)``

## Input:

``````syms x t
diff(sin(x*t^4),t,2)``````

## Output:

As we can see, we have got the 2nd derivative of our input function w.r.t ‘t’, as expected.[Notice the arguments ‘t’ and ‘2’, for derivative w.r.t and nth derivative respectively]