Question

найдите производную функции у=1-2х2х+1

Answer 1

$y=frac{1-2x}{2x+1}\\y'=frac{(1-2x)'*(2x+1)-(1-2x)*(2x+1)'}{(2x+1)^{2}}=frac{-2(2x+1)-2(1-2x)}{(2x+1)^{2}}=frac{-4x-2-2+4x}{(2x+1)^{2}}=-frac{4}{(2x+1)^{2}}$

Answer 2

$y=frac{1-2x}{2x+1}\\(frac{u}{v})'=frac{u'v-uv'}{v^2}\\y'=frac{-2cdot (2x+1)-(1-2x)cdot 2}{(2x+1)^2}=frac{-4x-2-2+4x}{(2x+1)^2}=-frac{4}{(2x+1)^2}$