## Calculus (3rd Edition)

$$z_x=4x^3y+y^{-2},\quad z_y=x^4-2xy^{-3}.$$
Recall that $(x^n)'=nx^{n-1}$ Since $z=x^4y+xy^{-2}$, then we have $$z_x=4x^3y+y^{-2},\quad z_y=x^4-2xy^{-3}.$$