**Here are some working rules used in Differential Calculus for solving any problem :-**

**Working Rule for Differentiation of Implicit Function**

1) Differentiate the given relation between

*and*

**x***with respect to*

**y**

**x .**2) Bring the terms containing

*on one side .*

**dy/dx**3) Divide both side by co-efficient of

*, this will give*

**dy/dx***.*

**dy/dx**4) In order to simplify the value of

*, use the relation between*

**dy/dx***and*

**x***.*

**y****Working Rule for Inverse Circular Functions**

Simplify the given expression , For example ;

If

*it is to be differentiated then put*

**(1/tan) z***in the form of*

**z***;*

**tan(theta)**So that ;

**[1/tan z] = [1/tan] [tan(theta)] = theta .**For this certain substitutions are helpful , they are ;

If

*occurs*

**square of a - square of x**put

*or*

**x=a sine(theta)**

**a cos(theta)**If

*occurs*

**square of a + square of x**put

*or*

**x=a tan(theta)**

**a cot(theta)**If

*occurs*

**square of x - square of a**put

*or*

**x=a sec(theta)**

**a cosec(theta)**If

*occurs*

**(a+x)/(a-x) or (a-x)/(a+x)**put

**x=a cos(2theta) .**If you follow this working rules you will see that the solution of problem in differential calculus will be easy . If anyone need that working rules are help them to solve the problem then from my next blog we will discuss many working rules like this .

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