Question

find f(x).
f(x)=\frac{ln x}{14 + x}
f(x)=square
(type an exact answer.)

Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y^\prime=\frac{u^\prime v - uv^\prime}{v^{2}}$. Here, $u = \ln x$ and $v=14 + x$.

Step2: Find $u^\prime$ and $v^\prime$

The derivative of $u=\ln x$ with respect to $x$ is $u^\prime=\frac{1}{x}$, and the derivative of $v = 14 + x$ with respect to $x$ is $v^\prime=1$.

Step3: Apply the quotient - rule

Substitute $u$, $v$, $u^\prime$, and $v^\prime$ into the quotient - rule formula:

$$
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$$

Answer:

$\frac{14 + x - x\ln x}{x(14 + x)^{2}}$