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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 .