How do you differentiate #sqrt(e^(x-y^2)-(xy)^2#?
You've presented a three dimensional function for differentiation. The common method of presenting a "derivative" for such a function is to use the gradient:
So we'll compute each partial individually and the result will be the gradient vector. Each can be easily determined using the chain rule.
From here, denoting the gradient is as easy as incorporating these into the gradient vector: