COMEDK · Maths · 26. Differentiation
\(\text { If } y=\sin ^{-1}(\sqrt{\sin x}) \text {, then } \dfrac{d y}{d x} \text { equals }\)
- A \(\dfrac{1}{2} \sqrt{1+\operatorname{cosec} x}\)
- B \(\dfrac{1}{2} \sqrt{1-\sin x}\)
- C \(\dfrac{1}{2} \sqrt{1-\operatorname{cosec} x}\)
- D \(\dfrac{1}{2} \sqrt{1+\sin x}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{1}{2} \sqrt{1+\operatorname{cosec} x}\)
Step-by-step Solution
Detailed explanation
\(\dfrac{dy}{dx} = \dfrac{1}{\sqrt{1 - \sin x}} \cdot \dfrac{\cos x}{2\sqrt{\sin x}} = \dfrac{\cos x}{2\sqrt{\sin x(1 - \sin x)}}\) Using \(\cos^2 x = 1 - \sin^2 x = (1 - \sin x)(1 + \sin x)\):…
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