Question

Найдите f штрих(0), если f(x)=x/x-1

Answer 1

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

$f'(0)= \frac{1}{(0-1)^2} = \frac{1}{1} =1$