Question

How do you use the limit definition of the derivative to find the derivative of f(x)=1/x?

Answer 1

Example 1. Let us start with the functionf(x) = x2. We have 




So 




which means f '(a) = 2a.

What about the derivative of f(x) = xn. Similar calculations, using the binomial expansion for (x+y)n (Pascal's Triangle), yield