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 x and y with respect to x .
2) Bring the terms containing dy/dx on one side .
3) Divide both side by co-efficient of dy/dx , this will give dy/dx .
4) In order to simplify the value of dy/dx , use the relation between x and y .
Working Rule for Inverse Circular Functions
Simplify the given expression , For example ;
If (1/tan) z it is to be differentiated then put z in the form of tan(theta) ;
So that ; [1/tan z] = [1/tan] [tan(theta)] = theta .
For this certain substitutions are helpful , they are ;
If square of a - square of x occurs
put x=a sine(theta) or a cos(theta)
If square of a + square of x occurs
put x=a tan(theta) or a cot(theta)
If square of x - square of a occurs
put x=a sec(theta) or a cosec(theta)
If (a+x)/(a-x) or (a-x)/(a+x) occurs
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 .