NDA 2016 Maths · Mathematics · Derivatives · hard

If x=t^2 and y=t^3, then (d^2y)/(dx^2 at t=1 is

Single correct option

x=t^2

and

y=t^3

, then

\dfrac{d^2y}{dx^2}

t=1

Show answer and solution

Answer: (D) $\dfrac34$

\dfrac{dy}{dx}=\dfrac{3t^2}{2t}=\dfrac{3t}2

. Then

\dfrac{d^2y}{dx^2}=\dfrac{d}{dt}\!\left(\dfrac{3t}{2}\right)\Big/\dfrac{dx}{dt}=\dfrac{3/2}{2t}=\dfrac34

t=1

. Stopping at

3/2

forgets to divide by

dx/dt

Original question written in the NDA 2016 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