First-Order Partial Derivatives

Calculate the first-order partial derivative of the following:

http://dammserv.loopback.nu/latex/im...727_HJhCAW.png

http://dammserv.loopback.nu/latex/im...727_WMExIH.png for all (x,y) in $\displaystyle R^2$

I used this as a composition function and used the chain rule.

http://dammserv.loopback.nu/latex/im...727_pVjxzr.png

However, I am unsure of how to apply this formula.

First-order partial derivative of x would be

http://dammserv.loopback.nu/latex/im...727_CS1jty.png

First-order pairtal derivative of y would be

http://dammserv.loopback.nu/latex/im...727_fX75s3.png

My question is http://dammserv.loopback.nu/latex/im...727_KIdP5w.png: how to compute this? Do I do another composition+chain rule?

Thank you.