#### Answer

$$f_x = 4x^3 + 3y^3$$
$$f_y = 15xy^2$$

#### Work Step by Step

To find $f_x$, we treat $y$ as a constant and differentiate with respect to $x$. Thus
$$f_x = 4x^3 + 3y^3.$$
Similarly, to find $f_y$, we treat $x$ s a constant and differentiate with respect to $y$. Thus
$$f_y = 15xy^2.$$