Question

Найти походную функции y=x-1/x+1+x+1/x-1

Answer 1

ПРОИЗВОДНАЯ функции.

$y=\dfrac{x-1}{x+1}+\dfrac{x+1}{x-1}\ \ ,\ \ \ \ \ \boxed{\ \Big(\dfrac{u}{v}\Big)'=\dfrac{u'v-uv'}{v^2}\ } \\\\\\y'=\dfrac{(x+1)-(x-1)}{(x+1)^2}+\dfrac{(x-1)-(x+1)}{(x-1)^2}=\dfrac{2}{(x+1)^2}-\dfrac{2}{(x-1)^2}=\\\\\\=\dfrac{2(x^2-2x+1)-2(x^2+2x+1)}{(x+1)^2(x-1)^2}=\dfrac{-8x}{(x+1)^2(x-1)^2}$