Let f(x)=sin⁡x,g(x)=x2 and h(x)=ln⁡x. if ϕ(x)=h(f(g(x))) then ϕ′′(x)= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
$2 x \cot x^{2}$
B
$2 \cot x^{2} - 4 x^{2} {cosec}^{2} x^{2}$
C
$2 \cot x^{2}$
D
$2 x \cot x$

Solution:

$ϕ (x) = h (f (g (x))) = \ln (\sin x^{2}) \Rightarrow ϕ^{'} (x) = \frac{1}{\sin x^{2}} (\cos x^{2}) . 2 x = c o t x^{2} . 2 x$
$ϕ^{"} (x) = c o t x^{2} . 2 + 2 x . (- \cos e c^{2} (x^{2}) . 2 x) = 2 c o t^{} x^{2} - 4 x^{2} \cos e c^{2} (x^{2})$

Let $f (x) = \sin x, g (x) = x^{2} and h (x) = \ln x . if ϕ (x) = h (f (g (x))) then ϕ^{''} (x) =$

Solution:

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