if $f(x,y) = \int_{x}^{y}p(p-1)(p-2)dp$ then calculate $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ How do i take derivative of this function : $f(x,y) = \int_{x}^{y}p(p-1)(p-2)dp$.
For single variable I can evaluate but this involves two variables. 
Any hint please I am stuck here.
I want to calculate the stationary points, so I would like to evaluate $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$.

Well,
\begin{align}
{\displaystyle \int \limits_x^y}p(p-1)(p-2)dp &= \frac{1}{4}\left(y^4-x^4\right)+x^3-y^3+y^2-x^2
\end{align}
Thus
\begin{align}
\frac{\partial f}{\partial x} &= \ldots \\
\frac{\partial f}{\partial y} &= \ldots
\end{align}
