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) = 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.