Last updated on Sep 22, 2026

f'(x)/f(x) (AQA A-Level Mathematics): Quizzes

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f'(x)/f(x)

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What is $\frac{f'(x)}{f(x)}$ the derivative of?

$\ln|f(x)|$

What is $\frac{d}{dx}[\ln|f(x)|]$ equal to?

$\frac{f'(x)}{f(x)}$

Which rule is used to find $\frac{d}{dx}[\ln|f(x)|]$ ?

Chain rule

What is $\int \frac{f'(x)}{f(x)} \, dx$ equal to?

$\ln|f(x)| + C$

If $f(x) = x^2 + 1$ , what is $\int \frac{2x}{x^2 + 1} \, dx$ ?

$\ln|x^2 + 1| + C$

In the example, if $f(x) = x^2 + 1$ , what is $f'(x)$ ?

$2x$

In the example with $f(x) = x^2 + 1$ , what is $\frac{f'(x)}{f(x)}$ ?

$\frac{2x}{x^2 + 1}$

By the chain rule, $\frac{d}{dx}[\ln|f(x)|]$ equals $\frac{1}{f(x)}$ multiplied by what?

$f'(x)$

The result $\int \frac{f'(x)}{f(x)} \, dx = \ln|f(x)| + C$ is useful for what?

Logarithmic differentiation & integration

What notation is used for the natural logarithm of $f(x)$ in the formula?

$\ln|f(x)|$

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