### Home > CALC > Chapter 5 > Lesson 5.5.2 > Problem 5-173

Use the definition of the derivative to write an expression (i.e. the limit of a difference quotient) representing each of the following derivatives. Then evaluate each limit to find the actual derivative. L'Hôpital's Rule may be used.

, where. Setup the definition of the derivative as a limit.

This is Hana's Method:Make a choice about how to evaluate this limit. These are your choices:

1) Use Algebra. Simplify the fraction until you can 'cancel out' thein the denominator and then evaluate as.

2) Deconstruct Hana's Method. Once you identify, findusing the Power Rule. Of course, in this case, that is working in circles.

3) Use l'Hôpital's Rule; after all, there is ain the numerator and the denominator. , where.Refer to the hints in part (a).

, where. Refer to the hints in part (a).