Question

Let f(x) = ln(1 − 2x). Which of the following represents f '(x) for all values of x for which the function is defined?

Answer 1

If you take $u=1-2x$, then by the chain rule

$f'(x)=\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm du}\cdot\dfrac{\mathrm du}{\mathrm dx}=\dfrac1u\cdot(-2)=-\dfrac2u=-\dfrac2{1-2x}$

so the answer is A.