Partial derivative of a function of several variables is its derivative with respect to one of those variables, keeping other variables as constant.

**Partial Derivatives**

Partial derivative of a function
of several variables is its derivative with respect to one of those variables,
keeping other variables as constant. In this section, we will restrict our
study to functions of two variables and their derivatives only.

Let *u* = *f* ( *x*
, *y*)
be a function of two independent variables *x* and *y*.

The derivative of *u* with respect to *x* when *x* varies and *y* remains constant is called the **partial
derivative of** *u***with respect
to** ** x,**
denoted by

provided the limit exists. Here âˆ†*x* is a small change in *x*

The derivative of *u* with respect to *y*, when *y* varies and *x* remains constant is called the **partial
derivative of** *u***with respect
to** ** y,**
denoted by

provided the limit exists. Here âˆ†*y* is a small change in *y*.

The process of finding a partial
derivative is called **partial differentiation.**

Tags : Applications of Differentiation , 11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation

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11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation : Partial Derivatives | Applications of Differentiation

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