Thursday, 13 February 2014

Some Working Rules in Calculus


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    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     .

Working Rule for Inverse Circular Functions

Simplify the given expression , For example ;
If   (1/tan) z   it is to be differentiated then put    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 .

No comments:

Post a Comment

Our Latest Post

How to find log (alpha+ i beta), Where alpha and beta are real

Here is the video to show the details of solving this problem. It is an important problem for basic understanding about the logarithm of re...

Popular Post