### Home > CALC > Chapter 3 > Lesson 3.4.3 > Problem 3-175

3-175.

Use the *definition of a derivative *as a limit to find the slope function, , of

*. Confirm your slope function with the Power Rule. Then use your slope function to find*

*and*

*.*

Hana's definition of the derivative:

1. Substitute into Hana's definition

2. Expand the numerator

3. Combine like terms

4. Factor out an

5. Cancel out the

6. Evaluate the limit as

This is

Use the Power Rule to find . Compare to the

*you found algebraically. If they do not agree, you probably made an algebraic error.*

Evaluate and

*.*