Re: show that mixed partials are equal

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.

Re: show that mixed partials are equal

I know how to take derivatives I'm just not use to the notation y'all are using

Re: show that mixed partials are equal

It's pretty standard notation:

$\displaystyle f_x= \frac{\partial f}{\partial x}$

$\displaystyle f_y= \frac{\partial f}{\partial y}$

The notation $\displaystyle D_x$ and $\displaystyle D_y$ is also used but less commonly.

Re: show that mixed partials are equal

I'm not familiar with the summation notation