### Home > APCALC > Chapter 8 > Lesson 8.3.3 > Problem8-129

8-129.

Multiple Choice: Given $f ( x ) = \operatorname { ln } | 4 - x ^ { 2 } |$, $f^\prime(x)$ is: Homework Help ✎

1. $| \frac { - 2 x } { 4 - x ^ { 2 } } |$

1. $| \frac { 2 x } { 4 - x ^ { 2 } } |$

1. $\frac { 2 x } { | x ^ { 2 } - 4 | }$

1. $\frac { 2 x } { x ^ { 2 } - 4 }$

1. $\frac { 1 } { | x - 2 | }$

Rewrite $f(x)$ as a piecewise-defined function with boundary points at $x = -2$ and $x = 2$. There will be three pieces. Though each piece needs to be differentiated separately, you will find that all three pieces have the same derivative!