Question

Найти частные производные по x и по y от функции....(100б)

Answer 1

$z=arctg(\frac{y}{x})\\\\\frac{\partial z}{\partial x}=(arctg(\frac{y}{x}))' =\frac{1}{1+(\frac{y}{x})^2 }*(-y*\frac{1}{x^2})=\frac{-y}{x^2+y^2} \\\\\frac{\partial z}{\partial y}=\frac{1}{1+(\frac{y}{x})^2 }*\frac{1}{x} =\frac{x}{x^2+y^2}}$