Question

hw14 - derivatives of logs section 2.9: problem 1 (1 point)
let
$f(x)=3\ln(7x)$.
$f(x)=\square$
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Explanation:

Step1: Recall derivative of $\ln(u)$

The derivative of $\ln(u)$ with respect to $x$ is $\frac{u'}{u}$ by the chain - rule. Here $u = 7x$ and the function is $y=3\ln(7x)$.

Step2: Find derivative of $u = 7x$

The derivative of $u = 7x$ with respect to $x$ is $u'=7$.

Step3: Apply the formula for $y = 3\ln(7x)$

Since $y = 3\ln(7x)$, by the constant - multiple rule of differentiation and the chain - rule, $y'=3\times\frac{7}{7x}$.

Step4: Simplify the expression

$3\times\frac{7}{7x}=\frac{3}{x}$.

Answer:

$\frac{3}{x}$