Question

If $y={\log }_{e^x}(x-2{)}^2$ for $x\ne 0,2$, then $y^{\prime }\left(3\right)$ is equal to

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{5}{3}$

Answer 1

The correct option is B $\frac{2}{3}$

$y=\frac{2\log (x-2)}{x}$
$\frac{dy}{dx}=-\frac{2\log (x-2)}{x^2}+\frac{2}{x(x-2)}$

$\frac{dy}{dx}{|}_{x=3}=0+\frac{2}{3}$