Let $f(x) = e^{-x^Tx},$ where $x \in \mathbb{R}^n$. What will be the second derivative?
The first is $~f'(x) = 2x^T e^{-x^Tx}$, and when I try to find the second, I confuse.
It will be $$f''(x) = 2e^{-x^Tx}\cdot \mathbb{E}_n-4x^Txe^{-x^Tx}$$ or $$f''(x) = 2e^{-x^Tx}\cdot \mathbb{E}_n-4||x||e^{-x^Tx}\cdot \mathbb{E}_n$$
And can you explain why?