## Calculus (3rd Edition)

$$f_x=\frac{\partial f}{\partial x}=4y^3,f_y=\frac{\partial f}{\partial y}=12xy^2.$$
To calculate the partial derivatives, treat all variables as constant except the variable we are deriving with respect to. Since $f(x,y)=4xy^3$, then we have $$f_x=\frac{\partial f}{\partial x}=4y^3,$$ $$f_y=\frac{\partial f}{\partial y}=12xy^2.$$