Question

√sin√x , then find the value of dy/dx
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Answer 1

$Let \: \: \: y = \sqrt{sin \sqrt{x} } \\ \frac{dy}{dx} = \frac{d}{dx} \sqrt{sin \sqrt{x} } \\ = \frac{1}{2 \sqrt{sin \sqrt{x} } } \frac{d}{dx} sin \sqrt{x} \\ = \frac{1}{2 \sqrt{sin \sqrt{x} } } cos \sqrt{x} \frac{d}{dx} \sqrt{x} \\ = \frac{cos \sqrt{x} }{2 \sqrt{sin \sqrt{x} } } . \frac{1}{2 \sqrt{x} } \\ = \frac{cos \sqrt{x} }{4 \sqrt{x} \sqrt{sin \sqrt{x} } }$