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Your answer is not complete, as you need something after the last "plus". To give an answer that's still correct though, let's call it n:
If:
y = x2/(x2 + n)
dy/dx = [2x(x2 + n) - (2x + dn/dx) ] / (x2 + n)2
= (2x3 + 2nx - 2x - dn/dx) / (x4 + 2nx2 + n2)
= (2x3 + [2n - 2]x - dn/dx) / (x4 + 2nx2 + n2)
If n is a constant, then you can remove the term dn/dx, and simplify the term [2n - 2]x
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