$\text { Find the derivative of the function } f ( x ) = \frac { e ^ { x } - 4 } { e ^ { x } + 4 } \text {. Simplify your answer. }$
A)$\frac { 2 e ^ { 2 x } } { \left( e ^ { x } + 4 \right) ^ { 2 } }$
B)$\frac { - 8 e ^ { x } } { \left( e ^ { x } + 4 \right) ^ { 2 } }$
C)$\frac { 8 e ^ { x } } { \left( e ^ { x } + 4 \right) ^ { 2 } }$
D) $\frac { 2 e ^ { 2 x } + 8 e ^ { x } } { \left( e ^ { x } + 4 \right) ^ { 2 } }$
E)$\frac { 1 } { \left( e ^ { x } + 4 \right) ^ { 2 } }$

Question

$\text { Find the derivative of the function } f ( x ) = \frac { e ^ { x } - 4 } { e ^ { x } + 4 } \text {. Simplify your answer. }$ 
A)$\frac { 2 e ^ { 2 x } } { \left( e ^ { x } + 4 \right) ^ { 2 } }$
B)$\frac { - 8 e ^ { x } } { \left( e ^ { x } + 4 \right) ^ { 2 } }$
C)$\frac { 8 e ^ { x } } { \left( e ^ { x } + 4 \right) ^ { 2 } }$
D) $\frac { 2 e ^ { 2 x } + 8 e ^ { x } } { \left( e ^ { x } + 4 \right) ^ { 2 } }$
E)$\frac { 1 } { \left( e ^ { x } + 4 \right) ^ { 2 } }$

Quizplus · Accepted Answer

We will use the quotient rule: 
\begin{align*}
\frac{d}{dx}\left(\frac{e^x-4}{e^x+4}ight) &= \frac{(e^x+4)\frac{d}{dx}(e^x-4)-(e^x-4)\frac{d}{dx}(e^x+4)}{(e^x+4)^2} \
&= \frac{(e^x+4)(e^x)-(e^x-4)(e^x)}{(e^x+4)^2} \
&= \frac{8e^x}{(e^x+4)^2}.
\end{align*} Therefore, the answer is $\boxed{	extbf{(C)}}$.

Find the derivative of the function f(x)=ex−4ex+4. Simplify your answer. \text { Find the derivative of the function } f ( x ) = \frac { e ^ { x } - 4 } { e ^ { x } + 4 } \text {. Simplify your answer. } Find the derivative of the function f(x)=ex+4ex−4​. Simplify your answer.

$\text { Find the derivative of the function } f ( x ) = \frac { e ^ { x } - 4 } { e ^ { x } + 4 } \text {. Simplify your answer. }$