Question

question what is the first derivative of $q(x)=(3x)^{7x}$ at $x = 2$? select the correct answer below: 14(613) 614(7ln6 + 7) 614(3ln6) 614(7ln6+\frac{7}{3})

Explanation:

Step1: Recall power - rule for differentiation

If $y = u^n$, then $y^\prime=nu^{n - 1}u^\prime$. Let $u = 3x$ and $n = 14$.
The derivative of $u = 3x$ with respect to $x$ is $u^\prime=3$.
So the derivative of $y=(3x)^{14}$ is $y^\prime = 14(3x)^{13}\times3=42(3x)^{13}$.
Evaluating at $x = 2$, we first note that when $x = 2$, $3x=6$.
The derivative at $x = 2$ is $42\times6^{13}=14\times3\times6^{13}=14\times6^{14}$.

Answer:

$14(6^{14})$