Find the derivative of the following function. $y = \ln x ^ { 5 }$
A) $\frac { 1 } { x }$
B) $\frac { 5 } { x }$
C) $\frac { 1 } { 5 x }$
D) $\frac { 1 } { x ^ { 2 } }$
E) $\frac { 1 } { 5 x ^ { 2 } }$

Question

Quizplus · Accepted Answer

The derivative of $y = \ln x^5$ can be found by applying the chain rule. The derivative of $\ln u$ is $\frac{1}{u}\frac{du}{dx}$, where $u = x^5$. Thus, the derivative is $\frac{1}{x^5} \cdot 5x^4 = \frac{5}{x}$.

Find the Derivative of the Following Function y=ln⁡x5y = \ln x ^ { 5 }y=lnx5

Find the Derivative of the Following Function $y = \ln x ^ { 5 }$