Answer
$\dfrac{d^2y}{dx^2} = 16x^2e^{-2x^2}-4x^{-2x^2}$
Work Step by Step
$y = e^{-2x^2}$
Chain Rule:
$\dfrac{dy}{dx} = -4xe^{-2x^2}$
Product Rule and Chain Rule:
$\dfrac{d^2y}{dx^2} = -4e^{-2x^2}+-4x(-4x)(e^{-2x^2}) = 16x^2e^{-2x^2}-4x^{-2x^2}$
