If the limit definition of a derivative can be used to find f ' , then what is the purpose of using other rules to find f '

Question

If the limit definition of a derivative can be used to find f ' , then what is the purpose of using other rules to find f '

Answer 1

IT is faster and easier than using the definition.

 

EX.

 

       y = x^2 ---> y' = 2x

 

     It is faster to do it that way than:

 

   lim (  (x+h)^2 - x^2)/ h ) as h-->0

          

      x^2 + 2xh + h^2 - x^2

     ---------------------------- 

                 h

 

           2xh + h^2

         ----------------

                  h

 

            2x + h

 

 

So the derivative is 2x as h-->-

 

THat took 3 steps at least as opposed to

being able to get the derivative by applying

the power rule, where you can actually look

at it and find the derivative.