dz/dx = 2(y - 4x)*(-4) + [m]\frac{8x}{2\sqrt{4x^2 + 2y^2}}[/m] = -8(y - 4x) + [m]\frac{4x\sqrt{4x^2 + 2y^2}}{4x^2 + 2y^2}[/m]
dz/dy = 2(y - 4x)*1 + [m]\frac{4y}{2\sqrt{4x^2 + 2y^2}}[/m] = 2(y - 4x) + [m]\frac{2y\sqrt{4x^2 + 2y^2}}{4x^2 + 2y^2}[/m]
Полный дифференциал:
dz = (32x -8y + [m]\frac{4x\sqrt{4x^2 + 2y^2}}{4x^2 + 2y^2}[/m]) dx + (2y - 8x + [m]\frac{2y\sqrt{4x^2 + 2y^2}}{4x^2 + 2y^2}[/m]) dy