The SLUTsky Equation

[ku]

$x=\frac{m}{2p_{x}}$ and $x^{h}=\sqrt{u\frac{p_{y}}{p_{x}}}$.

 

How do I show that $\frac{\partial{x}}{\partial{p_{x}}}=\frac{\partial{x^{h}}}{\partial{p_{x}}}-\frac{\partial{x}}{\partial{m}}x$?

[ku]

I forgot to add that $U(x,y)=xy$. It's very easy now. All that needs to be done is to show that RHS=LHS.