Let $f(x)=\sin x, g(x)=x^2$ and $h(x)=\log _e x$. If F(x) = (hog of)(x), then F''(x) is equal to
Answer & explanation
Correct answer: option 4
We have,
F(x) = (hogof)(x)
$\Rightarrow F(x) = h \{g(f(x)\}=h\{g(\sin x)\}=h\left(\sin ^2 x\right)$
$\Rightarrow F(x)=\log _e \sin ^2 x=2 \log _e \sin x$
$F'(x)=2 \cot x$ and $f''(x)=-2 ~cosec^2 x$