Differentiation Question 65

Question: If $ y=\sqrt{\sin \sqrt{x}} $ , then $ \frac{dy}{dx}= $

[MP PET 1997]

Options:

A) $ \frac{1}{2\sqrt{\cos \sqrt{x}}} $

B) $ \frac{\sqrt{\cos \sqrt{x}}}{2x} $

C) $ \frac{\cos \sqrt{x}}{4\sqrt{x}\sqrt{\sin \sqrt{x}}} $

D) $ \frac{1}{2\sqrt{\sin x}} $

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Answer:

Correct Answer: C

Solution:

$ \frac{dy}{dx}=\frac{1}{2\sqrt{\sin \sqrt{x}}}\times \cos \sqrt{x}\times \frac{1}{2\sqrt{x}} $ .