Question

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

Explanation:

Step1: Use log - derivative formula

$y = \log_2(u)=\frac{\ln u}{\ln 2}$, then $y^\prime=\frac{1}{u\ln 2}\cdot u^\prime$. Here $u = 6x^{3}+3$, $u^\prime=18x^{2}$.

Step2: Calculate $g^\prime(x)$

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

Answer:

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