Trending September 2023 # How Does Matlab Derivative Work With Examples # Suggested October 2023 # Top 13 Popular | Uyenanhthammy.com

# Trending September 2023 # How Does Matlab Derivative Work With Examples # Suggested October 2023 # Top 13 Popular

You are reading the article How Does Matlab Derivative Work With Examples updated in September 2023 on the website Uyenanhthammy.com. We hope that the information we have shared is helpful to you. If you find the content interesting and meaningful, please share it with your friends and continue to follow and support us for the latest updates. Suggested October 2023 How Does Matlab Derivative Work With Examples

Introduction to 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.

Start Your Free Data Science Course

Hadoop, Data Science, Statistics & others

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 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:

df = diff (f, x)

Output:

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:

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:

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)

[Notice that we have passed ‘t’ as an argument. Diff function will now take the derivative w.r.t ‘t’]

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:

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]

Conclusion

[Notice the arguments ‘t’ and ‘2’, for derivative w.r.t and nth derivative respectively]

‘diff’ function is used in MATLAB to calculate the differentiation or derivative of a function. We can calculate the derivative w.r.t the default variable or the variable we pass as an argument. Also, the degree of differentiation or derivative can be controlled using the argument.

Recommended Articles

This is a guide to MATLAB Derivative. Here we discuss how does MATLAB Derivative work along with appropriate syntax and respective examples. You may also look at the following articles to learn more –

You're reading How Does Matlab Derivative Work With Examples

Update the detailed information about How Does Matlab Derivative Work With Examples on the Uyenanhthammy.com website. We hope the article's content will meet your needs, and we will regularly update the information to provide you with the fastest and most accurate information. Have a great day!