I just want to make sure I got this integration by parts thing right...

$\displaystyle \int \frac{\partial f}{\partial x}\frac{\partial x}{\partial y}\partial y=\frac{\partial f}{\partial x}x(y)-X(y)$

(where X(y) is the integral of x(y))

Does that look all right? And then the derivative of this result w.r.t. y would be...

$\displaystyle \frac{\partial f}{\partial x}\frac{\partial x}{\partial y}-x(y)$

Right?

Thanks

[Edit: Nevermind! I just realized that the first term in the integral can be treated as a constant, so no need for integration by parts.]

[Edit again: Nevermind the last edit. That was a bad idea. Nonetheless I have figured out the problem.]