Question

Second derivative of ln x with respect to sin x at x = π is –

• A. $\frac{1}{\pi^{2}}$
• B. – $\frac{1}{\pi^{2}}$
• C. $\frac{1}{\pi}$
• D. Does not exist

Answer 1

Answer: (B)

– $\frac{1}{\pi^{2}}$

Answer 2

y = ln x, u = sinx, $\frac{dy}{du}$ = $\frac{1}{x\cos x}$

$\frac{d^{2}y}{du^{2}}$ = $\frac { \mathrm { d } } { \mathrm { dx } }$ $\left( \frac{1}{x\cos x} \right)\frac{dx}{du}$