OK, so what have you got so far for...

differentiating your with respect to y (holding x constant) i.e.

... and...

differentiating your with respect to x (holding y constant) i.e.

...?

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Don't integrate - balloontegrate!

http://www.ballooncalculus.org/forum/top.php

Balloon Calculus Drawing with LaTeX and Asymptote!