### 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. Homework Help ✎

*f*′(*x*), where. *h*′(*x*), where*h*(*x*) = (*x*− 2)^{−2}.*g*′(4), 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' 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.

Refer to the hints in part (a).

Refer to the hints in part (a).