Question

Найти dy/dx
e^(x-y) = x/y

Answer 1

Ответ:

$\displaystyle e^{x-y}=\dfrac{x}{y}\\\\lne^{x-y}=ln\frac{x}{y}\\\\(x-y)lne=ln\frac{x}{y}\\\\x-y=ln\frac{x}{y}\\\\(x-y)'=(lnx-lny)'\\\\1-y'=\frac{1}{x}-\frac{y'}{y}\\\\\frac{y'}{y}-y'=\frac{1}{x}-1\\\\y'\cdot \Big(\frac{1}{y}-1\Big)=\frac{1}{x}-1\\\\y'\cdot \frac{1-y}{y}=\frac{1-x}{x}\\\\y'=\frac{y\cdot (1-x)}{x\cdot (1-y)}$