Question

полный дифференциал функции z=tgx/y

Answer 1

$dz = frac{partial z}{partial x}cdot dx+frac{partial z}{partial y}cdot dy \ frac{partial z}{partial x}= (z)'_x= frac{tgx'}{y}=frac{frac{1}{cos^2x}}{y}=frac{1}{ycdot cos^2x}\ frac{partial z}{partial y} = tgx cdot frac{1}{y}'=-frac{tgx}{y^2}\ dz=frac{1}{ycdot cos^2x}cdot dx-frac{tgx}{y^2}cdot dy$