Question

Найдите производную функции

Answer 1

$x=y+arctgy\\\\x'=y'+(arctgy)'\\\\1=y'+\frac{y'}{1+y^2}\\\\y'\cdot (1+\frac{1}{1+y^2})=1\\\\y'\cdot \frac{2+y^2}{1+y^2}=1\\\\y'=\frac{1+y^2}{2+y^2}$