f:[0,∞) → ℝ, f(x) = e^(x^2)

In order to prove that f is strictly increasing, do I have to show that f'(x) is always positive?

I think f'(x)=[(x^2)e^(x^2)]/e + 2xe^(x^2)lne

I could have gotten that horribly wrong, so correct me if I have.

Then how to prove that this is strictly positive?

Thanks.