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What is the derivative of tan (sin x)?
1. sec2(sin x) sin x
2. -sec2(sin x) cos x
3. sec2(sin x) cos x
4. cosec2(sin x) cos x

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Correct Answer - Option 3 : sec2(sin x) cos x

Concept:

Chain rule: \(\rm\frac{d}{d x}[f(g(x))]=f^{\prime}(g(x)) g^{\prime}(x)\)

\(\rm\frac{d}{d x}[\tan x]=sec^2 x\)

Calculation:

Here let, f(x) =  tan (sin x)

f'(x) = sec2(sin x) × \(\rm\frac{d}{d x}[\sin x]\)

= sec2(sin x) cos x

∴ The derivative of tan (sin x) is sec2(sin x) cos x.

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