Second Order Implicit Partial Derivatives

This problem is doing my head in...

If is defined implicitly as a function of and by the equation

,

find the values of and when and .

I've got and although these were worked out fairly quickly without double checking, but irregardless I can't for the life of me figure out how to get , and no amount of googling it or reading the textbook seems to yield any more information.

Any help would be hugely appreciated, as this question is part of my exam preparation, and knowing my luck, a similar question is likely to come up in the actual exam.