Question

Знайдіть f'(1), якщо f(x) = 1÷2-x

Answer 1

$f(x) = \frac{1}{2 - x} = {(2 - x)}^{ - 1}$

$f'(x) = - {(2 - x)}^{ - 2} \times (2 - x)' = \\ = - \frac{1}{ {(2 - x)}^{2} } \times ( - 1) = \frac{1}{ {(2 - x)}^{2} }$

$f(1) = \frac{1}{(2 - 1) {}^{2} } = 1$