Question

question
what is the first derivative of $q(x)=ln\frac{3}{2}x^{8}$?
select the correct answer below:
$q(x)=\frac{8}{x}$
$q(x)=\frac{x}{8}$
$q(x)=-\frac{8}{x}$
$q(x)=8x$

Explanation:

Step1: Use log - property

$q(x)=\ln\frac{3}{2}+\ln x^{8}=\ln\frac{3}{2}+8\ln x$

Step2: Differentiate term - by - term

The derivative of a constant $\ln\frac{3}{2}$ is 0, and the derivative of $8\ln x$ is $\frac{8}{x}$. So $q'(x)=\frac{8}{x}$.

Answer:

$q'(x)=\frac{8}{x}$