Example:
            Find, by definition, the derivative of function  with respect to .
Solution:
            Let
            I. Change  to  and  to
               
            II. Find  by subtraction
               
               
               
               
               
            III. Divide both sides by
               
               
               
            IV. Find the limit of  where
               
               
                 Which is the derivative of w.r.t .

Example:
            Find, by definition, the derivative of function  with respect to .
Solution:
            Let
            I. Change  to  and  to
               
            II. Find  by subtraction
               
               
               
               
               
               
               
               
            Using Binomial Series Expansion
               
               
               
               
               
            III. Divide both sides by
               
               
            IV. Find the limit of  where
               
               
               
                 Which is the derivative of  w.r.t .

Example:
            Find, by definition, the derivative of function  with respect to .
Solution:
            Let
            I. Change  to  and  to
               
            II. Find  by subtraction
               
               
               
               
               
            III. Divide both sides by
               
               
            IV. Find the limit of  where
               
               
               
                 Which is the derivative of  w.r.t .