Question

Let f(x) = sin x; g(x) = x2 and h(x) = log x. If u (x) = h (f (g (x))), then d2u/dx2 is

(A) 2 cos3 x

(B) 2 cot x2 – 4x2 cosec2 x2

(C) 2x cot x2

(D) –2 cosec2 x

Answer 1

Correct option (B) 2 cot x2 – 4x2 cosec2 x2

Explanation:

u(x) = h(f (g(x))) = h(f(x2 )) = h (sin x2 ) = log sin x2

Hence u' (x) = 2 x cot x2 and

u(x) = 2 cot x2 – 4x2 cosec2 x2 .