Answer
$$\frac{\partial{f}}{\partial{x}}=4(xy)^{3}+16xy,\quad\frac{\partial{f}}{\partial{y}}=3x^{4}y^{2}+8x^2$$
Work Step by Step
$$f(x,y)=x^{4}y^{3}+8x^{2}y$$
$$\frac{\partial{f}}{\partial{x}}=4(xy)^{3}+16xy,\quad\frac{\partial{f}}{\partial{y}}=3x^{4}y^{2}+8x^2$$