d^2y/dx^2 of e^4x + e^-x?

y = e^u

y' = u'e^u

dy/dx = 4e^4x - e^-x

d^2y/dx^2 = (4)(4)e^4x + e^-x

You have done the dy/dx incorrectly:

This should be 4e^4x - e^-x

Then d^2y/dx^2 is 16e^4x + e^-x