CPM Homework Help : CALC3RD Problem 8-129

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

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

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

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

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

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

Hint:

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!