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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If $y=\sqrt{\sin x+y}$, then $\frac{d y}{d x}$ is equal to
  • ✓
    $\frac{\cos x}{2 y-1}$
  • B
    $\frac{\cos x}{1-2 y}$
  • C
    $\frac{\sin x}{1-2 y}$
  • D
    $\frac{\sin x}{2 y-1}$
✓

Answer

Correct option: A.
$\frac{\cos x}{2 y-1}$
(a) : $y=\sqrt{\sin x+y} \Rightarrow y^2=\sin x+y$
Differentiating w.r.t. $x$, we get
$
2 y \frac{d y}{d x}=\cos x+\frac{d y}{d x} \Rightarrow \frac{d y}{d x}=\frac{\cos x}{2 y-1}
$

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