If f(x) = sin x, g(x) = x2, h(x) = log x and F(x) = (hogof)(x) then F''(x) is :
Answer & explanation
Correct answer: option 4
$F(x)= (h o g o f)(x)=h(g(f(x)))$
$=h(g(\sin x))=h\left(\sin ^2 x\right)=\log _e\left(\sin ^2 x\right)$
$=2 \log _e(\sin x)$
$\Rightarrow F'(x) 2 \cot x \Rightarrow f''(x)$ = -2 cosec2x
Hence (4) is correct answer.