Assuming $f(x,y) = 24xy + 4xy^2 + 3x^3$ and taking partial differentiation respect to $x$ and $y$ I found to be:

$$\dfrac{\partial f}{\partial x} = 24y + 4y^2 +9x^2 \\
\dfrac{\partial f}{\partial y} = 24x + 8xy$$