### Home > APCALC > Chapter 5 > Lesson 5.5.2 > Problem 5-174

Use the definition of derivative as a limit to write an expression representing each of the following derivatives. Then evaluate each expression to write the actual derivative. l’Hôpital’s Rule may be used. Homework Help ✎

, whereSetup 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' the*h*in the denominator and then evaluate as*h*→0.

2) Deconstruct Hana's Method. Once you identify*f*(*x*), find*f*'(*x*) using the Power Rule. Of course, in this case, that is working in circles.

3) Use l'Hôpital's Rule; after all, there is a 0 in the numerator and the denominator., whereRefer to the hints in part (a).

, whereRefer to the hints in part (a).