Question

Найти производную функции $lny+ \frac{x}{y} =0$

Answer 1

$\ln y=- \frac{x}{y} \\ (\ln y)'=(- \frac{x}{y})' \\ \frac{y'}{y} =- \frac{x'y-xy'}{y^2} \\ \frac{y'}{y} =\frac{xy'-y}{y^2}\\ y'=\frac{xy'-y}{y}\\ xy'-yy'=y\\ (x-y)y'=y\\ y'= \frac{y}{x-y}$