Question

What is the solution?

Answer 1

Answer:
`32e^(4x)`

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Work Shown:

Compute the first derivative

`y = 2e^(4x)\\\\\\(dy)/(dx) = (d)/(dx)\left[2e^(4x)\right]\\\\\\(dy)/(dx) = 2*(d)/(dx)\left[e^(4x)\right]\\\\\\(dy)/(dx) = 2*4e^(4x)\\\\\\(dy)/(dx) = 8e^(4x)\\\\\\`

Don't forget to apply the chain rule.

Now compute the second derivative

`(d^2y)/(dx^2) = (d)/(dx)\left[(dy)/(dx)\right]\\\\\\(d^2y)/(dx^2) = (d)/(dx)\left[8e^(4x)\right]\\\\\\(d^2y)/(dx^2) = 8*(d)/(dx)\left[e^(4x)\right]\\\\\\(d^2y)/(dx^2) = 8*4e^(4x)\\\\\\(d^2y)/(dx^2) = 32e^(4x)\\\\\\`