Question

Найдите f(g(x))', если

$f(x)=x^2-x$

$g(x)=\frac{1}{x}$

Answer 1

$(f(g(x)))' = f'(g(x)) * g'(x) = (\dfrac{2}{x}-1)' * (\dfrac{1}{x})' = -\dfrac{1}{x^2}*(\dfrac{2}{x}-1)=\dfrac{1}{x^2}-\dfrac{2}{x^3}$