Question

find f(x). f(x)=\frac{ln x}{17 + x} f(x)=square (type an exact answer.)

Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = \ln x$ and $v=17 + x$.

Step2: Find $u'$ and $v'$

The derivative of $u=\ln x$ with respect to $x$ is $u'=\frac{1}{x}$, and the derivative of $v = 17+x$ with respect to $x$ is $v' = 1$.

Step3: Apply the quotient - rule

Substitute $u$, $u'$, $v$, and $v'$ into the quotient - rule formula:

$$
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$$

Answer:

$\frac{17 + x-x\ln x}{x(17 + x)^{2}}$