Question

Let f(x) = sin x; g(x) = x² and h(x) = log x.

If u (x) = h (f (g (x))), then $\frac{d^{2}u}{dx^{2}}$ is

• A. 2 cos³ x
• B. 2 cot x² – 4x² cosec² x²
• C. 2x cot x²
• D. –2 cosec² x

Answer 1

Answer: (B)

2 cot x² – 4x² cosec² x²

Answer 2

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.