differentiation /differentiation rules/differentiation formula.

Ø What is Differentiation?🚩

Differentiation is used to find the rates of change of one quantity as compared to another .

There are number of rules of differentiation  in mathematics to find the differentiation of any function easily.

Differentiation generally represent by the expression dy/dx or f’(x).

dy/dx means if y= function of x(in other world ,y is equal to an equation that containing number of x),then the derivative of y is written as dy/dx means rate of change in y w.r.t. x.  

                              dy/dx =Differentiation of y w.r.tx

Ø Basic Rule of Differentiation :

·       General rule of differentiation :

If y=x^n   dy/dx= nx^n-1 where nεR , n≠0

           

Differentiation

·       The derivative of any constant is always zero .

If y=k, k= constant , then dk/dx=0 always

              

differentiation rule-1

  

·       In any equation a constant multiplied by a function then the derivative of this equation is equal to the constant multiplied by the derivative of function.

                        

differentiation rule -2

·       The derivative of sum of two function is equal to the sum of derivative.

                             

differentiation rule-3

   

  

·       The derivative of difference of two function is equal to the difference of derivative.

                         

differentiation rule-4

 

·       Derivative of two multiplied function :if y=f(x).g(x) ,then

                       

differentiation rule-5

·       Derivative when y=f(x)/g(x) ,then

                   

differentiation rule-6

       

Differentiation Example:-

Question-1

Find derivative of following function by applying basic rule of differentiation.

Differentiation

                   

       Solution:-

             

Differentiation

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