Question

ПОМОГИТЕ ПОЖАЛУЙСТА!!

Answer 1

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

Answer 2

Ответ:  

Производная дроби равна  $\bf \Big(\dfrac{u}{v}\Big)'=\dfrac{u'v-uv'}{v^2}$  .

В заданном примере  u=x+1  ,  v=x-1  .

$\bf y=\dfrac{x+1}{x-1}\\\\\\y'=\dfrac{(x+1)'(x-1)-(x+1)(x-1)'}{(x-1)^2}=\dfrac{1\cdot (x-1)-(x+1)\cdot 1}{(x-1)^2}=\\\\\\=\dfrac{x-1-x-1}{(x-1)^2}=-\dfrac{2}{(x-1)^2}$