Question

Найти производную : x+y=ln(x+y)

Answer 1

$x+y=ln(x+y)\\1+y'= frac{1}{x+y}cdot (1+y')\\y'- frac{y'}{x+y}= frac{1}{x+y} -1\\y'cdot (1-frac{1}{x+y})= frac{1}{x+y}-1\\y'=-1$