Question

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

Answer 1

$z=frac12cdotln(x^2+y^2)\dz=frac{partial z}{partial x}dx+frac{partial z}{partial y}dy\frac{partial z}{partial x}=frac12cdotfrac1{x^2+y^2}cdot2x=frac{x}{x^2+y^2}\frac{partial z}{partial y}=frac12cdotfrac1{x^2+y^2}cdot2y=frac{y}{x^2+y^2}\dz=frac{x}{x^2+y^2}dx+frac{y}{x^2+y^2}dy$