Find the derivative of $f ( x ) = 5 ^ { 4 x + 4 }$ .
A) $( 5 \ln 4 ) 5 ^ { 4 x + 4 }$
B) $( 4 \ln 5 ) 5 ^ { 4 x + 4 }$
C) $( \ln 5 ) 5 ^ { 4 }$
D) $( 4 x + 4 ) 5 ^ { 4 x + 3 }$

Question

Quizplus · Accepted Answer

The derivative of $f(x) = 5^{4x+4}$ can be found using the chain rule. The outer function is $a^u$ where $a = 5$ and the inner function is $u = 4x + 4$. The derivative of $a^u$ with respect to $u$ is $\ln(a) \cdot a^u$, and the derivative of $u$ with respect to $x$ is $4$. Therefore, the derivative of $f(x)$ is $(4 \ln 5) 5^{4x+4}$.

Find the Derivative Of f(x)=54x+4f ( x ) = 5 ^ { 4 x + 4 }f(x)=54x+4

Find the Derivative Of $f ( x ) = 5 ^ { 4 x + 4 }$