f'(x)/f(x) (Edexcel A-Level Mathematics): Flashcards

The derivative is $f'(x)/f(x)$.

You use the chain rule for differentiation.

It is the derivative of $\ln|f(x)|$.

The integral is $\ln|f(x)| + C$.

$f'(x) = 2x$.

$\ln(x^2 + 1) + C$; $u = x^2 + 1$ for substitution.

It converts products into sums to simplify integration.

It's $f'(x)/f(x)$ by the definition of logarithmic derivative.

Look for $f'(x)/f(x)$ in expressions.

$C$ is the constant of integration.