If y = √(sin x + y), then dy/dx equals. A.(cos x)/(2y - 1) B. (cos x)/(1 - 2y) C. (sin x)/(1 - 2y) D. (sin x)/(2y - 1)

Question

If y = \(\sqrt{sin\,\text x+y,}\) then \(\cfrac{dy}{d\mathrm x} \) equals.

A. \(\cfrac{cos\,\text x}{2y - 1}\)

B. \(\cfrac{cos\,\text x}{1-2y}\)

C. \(\cfrac{sin\,\text x}{1-2y}\)

D. \(\cfrac{sin\,\text x}{2y-1}\)

Answer 1

Correct option is A. \(\cfrac{cos\,\text x}{2y - 1}\) 

y = \(\sqrt{sin\,\text x+y}\) 

Squaring both sides, we get

y² = sin x + y

Differentiating w.r.t y we get