Solution
Given, $$y = \sqrt{x + y}$$
Squaring on both sides, we get
$$y^2=x+y$$
$$\Rightarrow$$ $$x=y^2-y$$
$$\Rightarrow$$ $$\frac{dx}{dy} = 2y^{2-1}-y^{1-1}$$
$$\Rightarrow$$ $$\frac{dx}{dy} = 2y-1$$
Hence, the correct answer is Option D
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