Answer: [tex]32e^{4x}[/tex]
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Work Shown:
Compute the first derivative
[tex]y = 2e^{4x}\\\\\\\frac{dy}{dx} = \frac{d}{dx}\left[2e^{4x}\right]\\\\\\\frac{dy}{dx} = 2*\frac{d}{dx}\left[e^{4x}\right]\\\\\\\frac{dy}{dx} = 2*4e^{4x}\\\\\\\frac{dy}{dx} = 8e^{4x}\\\\\\[/tex]
Don't forget to apply the chain rule.
Now compute the second derivative
[tex]\frac{d^2y}{dx^2} = \frac{d}{dx}\left[\frac{dy}{dx}\right]\\\\\\\frac{d^2y}{dx^2} = \frac{d}{dx}\left[8e^{4x}\right]\\\\\\\frac{d^2y}{dx^2} = 8*\frac{d}{dx}\left[e^{4x}\right]\\\\\\\frac{d^2y}{dx^2} = 8*4e^{4x}\\\\\\\frac{d^2y}{dx^2} = 32e^{4x}\\\\\\[/tex]
