Correct Answer - Option 3 : sec

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

= sec^{2}(sin x) cos x

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