so if u is a function, d/dx e^u = u' e^u

now we have y = 2e^(4x^4)

=> y'= 16x^3(2)e^(4x^4) = 32x^3 * e^(4x^4)

now for the second derivative we need the product rule:

=> y'' = 96x^2 * e^(4x^4) + 32x^3(16x^3)e^(4x^4)

=> y'' = 96x^2 * e^(4x^4) + 512x^6 * e^(4x^4)

=> y'' = 32x^2 * e^(4x^4) * [3 + 16x^4]