Find the derivative of the following function. $y = 8 + \ln 5 x$
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 $y = 8 + \ln(5x)$ with respect to $x$ is found using the chain rule. The derivative of a constant is 0, and the derivative of $\ln(u)$ is $\frac{1}{u}$ times the derivative of $u$, where $u = 5x$. The derivative of $5x$ with respect to $x$ is 5, but since the 5 is a constant multiplier of $x$ in the argument of the logarithm, it does not affect the differentiation of $\ln(5x)$ with respect to $x$, which results in $\frac{1}{5x} \cdot 5 = \frac{1}{x}$.

Find the Derivative of the Following Function y=8+ln⁡5xy = 8 + \ln 5 xy=8+ln5x

Find the Derivative of the Following Function $y = 8 + \ln 5 x$