Question

Найти dz/dx и dz/dy для y=cos^2x/2y

Answer 1

$z=cos^2frac{x}{2y}\\z'_{x}=2, cosfrac{x}{2y}cdot sinfrac{x}{2y}cdot frac{1}{2y}=frac{1}{2y}cdot sinfrac{x}{y} \\z'_{y}=2, cosfrac{x}{2y}cdot sinfrac{x}{2y}cdot frac{x}{2}cdot (-frac{1}{y^2}) =-frac{x}{2y^2}cdot sinfrac{x}{y}$