Find the derivative of the following function. $y = 8 ^ { 9 x + 1 }$
A) $y ^ { \prime } = ( 8 \ln 9 ) 8 ^ { 9 x + 1 }$
B) $y ^ { \prime } = ( 9 \ln 8 ) 8 ^ { 9 x + 1 }$
C) $ y ^ { \prime } = ( \ln 9 ) ^ { 9 x + 1 }$
D) $y ^ { \prime } = ( \ln 8 ) 8 ^ { 9 x + 1 }$
E) $y ^ { \prime } = ( \ln 72 ) 8 ^ { 9 x + 1 }$

Question

Quizplus · Accepted Answer

The derivative of $y = a^{u(x)}$ where $a$ is a constant and $u(x)$ is a function of $x$, is given by $y' = a^{u(x)} \ln(a) u'(x)$. Here, $a = 8$ and $u(x) = 9x + 1$, so $u'(x) = 9$. Therefore, the derivative is $y' = 8^{9x+1} \ln(8) \cdot 9$, which matches option B.

Find the Derivative of the Following Function y=89x+1y = 8 ^ { 9 x + 1 }y=89x+1

Find the Derivative of the Following Function $y = 8 ^ { 9 x + 1 }$