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**Need help with implicit differentiation**

I have only just been introduced to implicit differentiation and am cluelessly stuck on this question:

Express d^2y/dx^2 as a function of x if siny + cosy = x

my first attempt was just to simply differentiate each term, and ended up with -(siny+cosy)d^2y/dx^2 = 0. The answer in the back of the book is: x/(2-x^2)^(3/2)...which unlike my answer is a function of x...my problem is that I really don't know how to arrive at this answer.

I can't think of any trig identity that can help me here and so my best guess is that I should find the three sides of a triangle with which siny and cosy make x, but I have no idea about how to go about finding these sides with the information I have been given.

part of the denominator: sqrt(2-x^2) seems like the hypoteneuse but I am having difficulty coming up with the other two sides and to make x. I apologise if solving this should be a no-brainer but I simply don't know how to proceed. Can someone please point me in the right direction?

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