Question

Ln[sqrt(1-2x)/(1+2x)] найти производную

Answer 1

$(ln(\sqrt{\frac{1-2x}{1+2x}}))'=(\frac{1}2ln(\frac{1-2x}{1+2x}))'=\frac{1}2*\frac{1}{\frac{1-2x}{1+2x}}*(\frac{1-2x}{1+2x})'=\\\\=\frac 12*\frac{1+2x}{1-2x}*\frac{-2(1+2x)-2(1-2x)}{(1+2x)^2}=\frac 12*\frac{1+2x}{1-2x}*\frac{-2-4x-2+4x}{(1+2x)^2}=-\frac{2}{(1-2x)(1+2x)}$