4. [-/1 Points] DETAILS MY NO Differentiate the function. $$ y=\frac{13}{\ln (x)} $$ $$ y^{\prime}=\square $$

Question

UpStudy AI · Accepted Answer

Given the function

$$
y = \frac{13}{\ln(x)} = 13 \cdot (\ln(x))^{-1},
$$

we differentiate using the chain rule. The derivative of $$(\ln(x))^{-1}$$ is

$$
\frac{d}{dx} \left[(\ln(x))^{-1}\right] = -1 \cdot (\ln(x))^{-2} \cdot \frac{1}{x} = -\frac{1}{x(\ln(x))^2}.
$$

Thus, multiplying by 13 we obtain

$$
y' = 13 \cdot \left(-\frac{1}{x(\ln(x))^2}\right) = -\frac{13}{x(\ln(x))^2}.
$$
$$ y' = -\frac{13}{x(\ln(x))^2} $$

[-/1 Points] DETAILS MY NO
Differentiate the function.