Question

Проиводные ylnx-xlny=0

Answer 1

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

Ответ: $y' = \dfrac{y(x \ln y - y)}{x(y \ln x - x)}$