Question

what is a function that could have \\(-9 - \frac{13}{x}\\) as its derivative?

\\(f(x) = \\)

Explanation:

Identify the given derivative

Using the Antiderivatives knowledge point

$$ F'(x) = -9 - \frac{13}{x} $$

Integrate the constant term

Using the Antiderivatives knowledge point

$$ \int -9 \, dx = -9x $$

Integrate the rational term

Using the Antiderivatives knowledge point

$$ \int -\frac{13}{x} \, dx = -13\ln|x| $$

Combine the terms

Using the Antiderivatives knowledge point

$$ F(x) = -9x - 13\ln(x) $$

Answer:

What is a function that could have \(-9 - \frac{13}{x}\) as its derivative?

\(F(x) =\) <blank>\(-9x - 13\ln(x)\)</blank>