Are you saying that you do not know how to find a derivative of a polynomial? If you are taking a course with questions about partial derivatives, that would be very strange!

A general polynomial in x and y would be of the form, as Fernando Revilla said, $\displaystyle f(x,y)= \sum_{n\ge 0; m\ge 0} a_{mn}x^my^n$ with only a finite number of $\displaystyle a_{mn}$ non-zero.

Okay, what is $\displaystyle f_x$? What is $\displaystyle f_y$? Now differentiate $\displaystyle f_x$ with respect to y and $\displaystyle f_y$ with respect to x.