Find the derivative of the function. $r ( x ) = \ln \mid 4 x + e ^ { 4 x }$
A) $\frac { 4 + 4 e ^ { 4 x } } { 4 x + 4 e ^ { 4 x } }$
B) $\frac { 4 + 4 e ^ { 4 x } } { 4 x + e ^ { 4 x } }$
C) $\frac { 4 + e ^ { 4 x } } { 4 x + e ^ { 4 x } }$
D) $\frac { 4 + e ^ { 4 x } } { 4 x + 4 e ^ { 4 x } }$
E) none of these

Question

Find the derivative of the function.  $r ( x ) = \ln \mid 4 x + e ^ { 4 x }$  
A)  $\frac { 4 + 4 e ^ { 4 x } } { 4 x + 4 e ^ { 4 x } }$
B)   $\frac { 4 + 4 e ^ { 4 x } } { 4 x + e ^ { 4 x } }$
C)  $\frac { 4 + e ^ { 4 x } } { 4 x + e ^ { 4 x } }$
D)  $\frac { 4 + e ^ { 4 x } } { 4 x + 4 e ^ { 4 x } }$
E) none of these

Quizplus · Accepted Answer

The derivative of $r(x) = \ln |4x + e^{4x}|$ using the chain rule is $r'(x) = \frac{1}{4x + e^{4x}} \cdot (4 + 4e^{4x})$, which simplifies to $\frac{4 + 4e^{4x}}{4x + e^{4x}}$.

Find the Derivative of the Function r(x)=ln⁡∣4x+e4xr ( x ) = \ln \mid 4 x + e ^ { 4 x }r(x)=ln∣4x+e4x

Find the Derivative of the Function $r ( x ) = \ln \mid 4 x + e ^ { 4 x }$