Question

question 13 · 1 point what is g(x) when g(x)=log₂(6x³ + 3)? select the correct answer below: (ln 2)(6x³+3) 18x² (ln 2)(6x³+3) 1 (ln 2)(18x²) 6x³+3 6x³+3 log₂(18x²)

Explanation:

Step1: Recall log - derivative formula

If $y = \log_a(u)$, then $y'=\frac{u'}{u\ln a}$. Here $a = 2$ and $u=6x^{3}+3$.

Step2: Find derivative of $u$

$u = 6x^{3}+3$, so $u'=18x^{2}$.

Step3: Calculate $g'(x)$

$g'(x)=\frac{18x^{2}}{(6x^{3}+3)\ln 2}$.

Answer:

$\frac{18x^{2}}{(6x^{3}+3)\ln 2}$