# Basic Laws of Differentiation

**Scalar multiple rule***f*(*x*) and*g*(*x*) be any two functions of*x*. Then, where,*c*is any constant

ExampleSolution

=*x***Sum and difference rule**

ExampleSolution**Product rule****(1st function Ã— 2nd function)**ExampleSolution**Quotient rule**

Example

Solution

Example

Solution

Example

Solution

Example

Solution

Example

Solution

If

*u*and*v*are two functions of*x*, then we know thatIn the given expression

Example

Solution

If

*u*and*v*are two functions of*x*, then we know thatIn the given expression

# Derivative of a Function

Let*y*=

*f*(

*u*), where

*u*=

*g*(

*x*)

Then

Example

Solution

In the given expression