JEE Main 2014 · 9 Apr · Shift 1 · Mathematics Q72

MathematicsSingle correct+4 / -1Question 72 of 90

If $y=e^{nx}$ , then $\left(\dfrac{d^2y}{dx^2}\right)\left(\dfrac{d^2x}{dy^2}\right)$ is equal to :

ne^{nx}

ne^{-nx}

-ne^{-nx}

Answer and worked solution

Official answer: D

$\dfrac{d^2y}{dx^2}=n^2e^{nx}$ .
$x=\dfrac{\ln y}n$ gives $\dfrac{d^2x}{dy^2}=-\dfrac1{ny^2}=-\dfrac{e^{-2nx}}{n}$ .

Product: $-ne^{-nx}$ .

JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 72