Partial Derivation

 

Introduction 

First Order Partial Derivatives 

Higher Order Partial Derivatives 

 

Introduction

In many cases a function depends on more than one independent variables. In order to calculate the derivative of this function, with respect to one variable, we make the calculations as usual, considering all the other variables as constants.

 

First Order Partial Derivatives

Example 1:

The partial derivative with respect to x is:

The partial derivative with respect to y is:

 

Example 2:

The partial derivative with respect to x is:

The partial derivative with respect to y is:

 

Example 3:

The partial derivative with respect to x is:

The partial derivative with respect to y is:

 

Higher Order Partial Derivatives

Example 1:

The partial derivatives with respect to x is:

The partial derivatives with respect to y is:

 

Example 2:

A double partial derivative with respect to both variables is: