Question

Найдите полный дифференциал функции z=(1/2)*ln(x^2+Y2)

Answer 1

$z=\frac12\cdot\ln(x^2+y^2)\\dz=\frac{\partial z}{\partial x}dx+\frac{\partial z}{\partial y}dy\\\frac{\partial z}{\partial x}=\frac12\cdot\frac1{x^2+y^2}\cdot2x=\frac{x}{x^2+y^2}\\\frac{\partial z}{\partial y}=\frac12\cdot\frac1{x^2+y^2}\cdot2y=\frac{y}{x^2+y^2}\\dz=\frac{x}{x^2+y^2}dx+\frac{y}{x^2+y^2}dy$