Question 135

If $$y = \sqrt{x + y}$$ then $$\frac{dx}{dy} =$$

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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