Question

Найдите производную функции f(x)= x^2 +2x/x-1

Answer 1

Ответ:

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

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