Question

найдите производную функции у=1-2х\2х+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

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