NDA 2024 Maths · Mathematics · Derivatives · medium

If y=sin (ln x) for x>0, then xdy/dx at x=e^π/3 is

Single correct option

y=\sin(\ln x)

for

x>0

, then

x\dfrac{dy}{dx}

x=e^{\pi/3}

Show answer and solution

Answer: (D) $\frac12$

By the chain rule

\frac{dy}{dx}=\cos(\ln x)\cdot\frac1x

, so

x\frac{dy}{dx}=\cos(\ln x)

. At

x=e^{\pi/3}

\ln x=\frac\pi3

and

\cos\frac\pi3=\frac12

. Trap:

\frac{\sqrt3}{2}

\sin\frac\pi3

(the value of

y

), and

\frac{1}{2e^{\pi/3}}

\frac{dy}{dx}

itself, not

x\frac{dy}{dx}

Original question written in the NDA 2024 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake