First slide

Diffrentiation

Question

$If f (x) = \sqrt{\sin \sqrt{x}}, then find f^{'} (x)$

Difficult

A

$\frac{1}{4} \frac{\cos \sqrt{x}}{\sqrt{\sin x}}$
B

$\frac{1}{4} \frac{\cos \sqrt{x}}{\sqrt{x} \sqrt{\cos \sqrt{x}}}$
C

$\frac{1}{4} \frac{\cot \sqrt{x}}{\sqrt{x} \sqrt{\sin \sqrt{x}}}$
D

$\frac{1}{4} \frac{\sqrt{\cot \sqrt{x}} \sqrt{\cos \sqrt{x}}}{\sqrt{x}}$

Solution

$f' (x) = \frac{1}{2} {(\sin \sqrt{x})}^{- \frac{1}{2}} \times \cos \sqrt{x} \times \frac{1}{2 \sqrt{x}}$

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