Example 3.1.  Use the limit definition to find the derivative of  .  

Solution.  Using Equation (3-1), we have  

              

We can drop the subscript on to obtain    as a general formula.

Explore Solution 3.1.

Enter the function f[z].

Form the difference quotient.

Observe that substitution of     indeterminate.

Calculate the derivative as the limit of the difference quotient.

Notice that the difference quotient can be simplified before substitution of    and can be used to find the derivative.

Hence we have used the limit definition to find the derivative of  f[z]  at the point  .  
Thus, the derivative of   .  

(c) 2006 John H. Mathews, Russell W. Howell