Home > APCALC > Chapter 4 > Lesson 4.5.1 > Problem4-177

4-177.

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

Show all algebraic steps. DO NOT use a shortcut!

Hana's Definition of the Derivative:

$f'(x)=\lim \limits_{h\rightarrow 0}{\frac{f(x+h)-f(x)}{h}}$

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.