Question

Найти производную функции у=е^1-x/1+x

Answer 1

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