I need help finding the second derivative of e^(1/x)

So, f'(x) = e^(1/x) * (d/dx)(1/x)

f'(x) = e^(1/x) * (d/dx)(1/x)

f'(x) = -1/(x^2) * e^(1/x)

Using the product rule where u = -1/(x^2) and v = e^(1/x)

f''(x) = -1/(x^2) * [-1/(x^2) * e^(1/x)] + e^(1/x) * [2/(x^3)]

f''(x) = 1/(x^4) * e^(1/x) + 2/(x^3) * e^(1/x)

I know I am close just can’t figure out the next step.