### Home > APCALC > Chapter 3 > Lesson 3.4.2 > Problem 3-169

3-169.

Use the *definition of a derivative as a limit* to write an equation for if

*. Use the Power Rule to confirm your answer.*

Hana's definition of the derivative:

Substitute into Hana's definition of the derivative.

Expand the numerator and combine like terms.

Factor out an from the numerator so you can 'cancel out' the

*from the denominator.*

Evaluate the limit as . This will give you

*.*

Confirm that the you found Algebraically agrees with what you get using the Power Rule.