If f(x) = sin x, g(x) = x2, h(x) = log x and F(x) = (hogof)(x) then F''(x) is :

2 cosec3x 2 cot x2 – 4x2cosec2x2 2x cot x2 –2 cosec2x

–2 cosec2x

$F(x)= (h o g o f)(x)=h(g(f(x)))$ $=h(g(\sin x))=h\left(\sin ^2 x\right)=\log _e\left(\sin ^2 x\right)$ $=2 \log _e(\sin x)$ $\Rightarrow F'(x) 2 \cot x \Rightarrow f''(x)$ = -2 cosec2x Hence (4) is correct answer.