Goseeko blog
  • Home
  • Engineering
    • Civil
    • Electronics
    • Computers
  • Science
    • Chemistry
    • Maths
    • Physics
  • Commerce
  • Arts
  • E-Learning
  • Career
  • Exams
  • Scholarships
  • Hiring News
  • Goseeko- Smart Study Material
@2021 - All Right Reserved. Designed and Developed by PenciDesign
Top Posts
Goseeko launches its own certifications for engineering and...
Online certifications which you can get in a...
What is Race around Condition?
What is a Development Plan ?
What is a Co-operative Bank?
What are the properties of Laser?
Top 5 Websites for Academic Research
What is regula-falsi method?
Top 10 Engineering YouTube Channels for Engineers
What is Lorentz Transformation?
What are Toposheets?
What is Pumping and its types?
Maths

What is partial differentiation?

by Team Goseeko 12/07/2021
written by Team Goseeko 12/07/2021 0 comment

Overview

We use partial differentiation in vector calculus and differential geometry.

When the function depends on two or more variables then the derivative changes into partial derivative.

A partial derivative of a function of several variables is an ordinary derivative with respect to one of the variables when all the other variables remain constant.

We use all the rules of differentiation but the condition is that if we are differentiating partially with respect to one variable, all the other variables are treated as constants.

Definition of Partial Differentiation

Suppose we have a function f(x, y), which is dependent on two variables x and y. x and y are independent of each other.

Then we will say that the function ‘f’ partially depends on these two variables.

The derivative of the function ‘f’ is called the partial derivative of ‘f’.

 Notations

Suppose we have a function u = f (x, y) of two independent variables x and y. If we keep y constant and x varies then function u becomes a function of x only. The derivative of u with respect to x, keeping y as constant is called partial derivative of ‘u’, with respect to ‘x’.

The following notations we use for partial differentiation-

Similarly, the partial derivative of ‘u’ with respect to ‘y’ keeping x as constant is denoted by

Product and quotient rules of partial derivative

Product rule:

If u = f(x, y).g(x, y), then 

And

Quotient rule:

If u = f(x, y)/g(x, y), then [note- g(x, y) should be non-zero]

And

Partial derivative of higher orders

Let u = f(x, y) then and will be the function of x and y, and these functions can again be differentiated partially with respect to x and y respectively.

These are called the second-order partial derivatives.

Note- 

Solved examples

Example: Differentiate the following function partially with respect to x and y.

Solution:

Here the function is-

Now differentiating partially with respect to ‘x’, we get-

Similarly differentiating partially with respect to ‘y’, we get-

Example: Find the value of of the following function-

Solution:

Here we have-

First we will partially differentiate the given function with respect to ‘z’

Now

Finally

Which can be written as-

Interested in learning about similar topics? Here are a few hand-picked blogs for you!

  • What is Hypothesis?
  • What is Differentiation?

Share
0
FacebookTwitterPinterestLinkedinTumblr
previous post
Top 5 Websites for Academic Research
next post
What are homogeneous differential equations?

You may also like

What are matrices and their types?

16/05/2022

What is graph theory?

16/05/2022

What is a ring?

16/05/2022

What are the definite and indefinite integrals? Explained...

29/04/2022

What is simplex method?

20/04/2022

What is maxima and minima?

20/04/2022

What is the sample space and types of...

20/04/2022

What is the Pigeonhole principle?

20/04/2022

What is a bar diagram?

20/04/2022

What is correlation?

15/04/2022

Leave a Comment Cancel Reply

Save my name, email, and website in this browser for the next time I comment.

Keep in touch

Facebook Twitter Instagram Youtube

Popular Posts

  • 1

    What is Race around Condition?

    03/08/2021
  • 2

    What is a Development Plan ?

    02/08/2021
  • 3

    What is a Co-operative Bank?

    03/08/2021
  • 4

    What are the properties of Laser?

    02/07/2021
  • 5

    Top 5 Websites for Academic Research

    11/07/2021
  • 6

    What is regula-falsi method?

    03/08/2021
  • 7

    Top 10 Engineering YouTube Channels for Engineers

    10/07/2021
  • 8

    What is Lorentz Transformation?

    02/07/2021
  • 9

    What are Toposheets?

    07/07/2021
  • 10

    What is Pumping and its types?

    03/08/2021

Categories

  • Arts
  • Career
  • Chemistry
  • Civil
  • Commerce
  • Computers
  • E-Learning
  • Electronics
  • Engineering
  • Exams
  • Hiring News
  • Maths
  • Physics
  • Scholarships
  • Uncategorized

Read alsox

What is regula-falsi method?

03/08/2021

What is conditional Probability?

26/05/2021

What is an analytic function?

03/08/2021