Answer
$f_x=4x^3+5y^3$, $f_y=15xy^2$.
Work Step by Step
$f(x,y)=x^4+5xy^3$
To find $f_x$ we treat y as a constant and differentiate with respect to $x$.
$f_x=4x^3+5y^3$
To find $f_y$ we treat x as a constant and differentiate with respect to $y$.
$f_y=15xy^2$
