CPM Homework Help : CALC Problem 4-166

Use the definition of a derivative as a limit to find $\frac { d } { d x } ( \frac { 2 } { x ^ { 2 } } )$ .

Hint:

Show all algebraic steps. DO NOT use a shortcut!
Hana's Definition of the Derivative:

Steps:

1. Substitute.
2. Expand the numerator.
3. Combine like terms.
4. Factor out an $h$ .
5. Cancel out the $h$ in the denominator.
6. Evaluate the limit.
7. Confirm your answer with the Power Rule.