Question

question determine the derivative of $g(x)=log_4(x^{2}-9x)$. provide your answer below: $2x - 9$

Explanation:

Step1: Use log - derivative formula

$g(x)=\log_4(u)$ where $u = x^{2}-9x$, and $\frac{d}{dx}\log_a(u)=\frac{1}{u\ln(a)}\cdot\frac{du}{dx}$.

Step2: Differentiate $u$

$\frac{du}{dx}=\frac{d}{dx}(x^{2}-9x)=2x - 9$.

Step3: Find $g'(x)$

$g'(x)=\frac{2x - 9}{(x^{2}-9x)\ln(4)}$.

Answer:

$\frac{2x - 9}{(x^{2}-9x)\ln(4)}$