Some Important Differential Terms

 


Logarithmic Differentiation :- 

In order to differentiate a function of the form     v power on u    , where    u, v   are both variables , it is necessary to take its logarithm and then differentiate . This process which is known as Logarithmic Differentiation is also useful when the function to be differentiated is the product of a number of factors .


Preliminary Transformation :- 

In some cases , a preliminary transformation of the function to be differentiated facilitates the process differentiation a good deal .


Differentiation "ab into" :- 

To differentiate "ab into" or from first principles means that the process of differentiation is to be performed without making any use of the theorems on the differentiations of sums , products functions and functions etc. nor is any use to be made of the differential co-officiants of standard  forms  .


The   n th  derivative of the product of the powers of  sines and cosines :-

In order to find out   n th  derivative of such a product , we have to express it as the some of the sines and cosines of multiples of the independent variables .