Z=x×㏑[latex] \frac{x}{y} [/latex] найти x([latex] \frac{dz}{dx} [/latex])+y([latex] \frac{dz}{dy} [/latex])=0 если моно то по подробнее

[latex]z=x\cdot ln\frac{x}{y}\\\\\frac{\partial z}{\partial x}=ln \frac{x}{y} +x\cdot \frac{y}{x} \cdot \frac{1}{y}=ln \frac{x}{y} +1\\\\\frac{\partial z}{\partial y}=x\cdot \frac{y}{x}\cdot (\frac{-x}{y^2})=-\frac{x}{y}\\\\\\x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}=x(ln \frac{x}{y} +1)-y\cdot \frac{x}{y} =xln \frac{x}{y} [/latex]