Let a $\theta$ be a 2 Dimensional vector and $\alpha$, $\beta$ be positive scalars. Let $f(\theta)$ be a function given as:
$ f(\theta) = \alpha \exp(-\beta \: \theta^T \theta)$
I can find the gradient of the function using the chain rule but I am having some difficulty in finding the Hessian. The gradient which I computed is the following:
$\nabla f(\theta) = - 2 \alpha \beta \exp(-\beta \: \theta^T \theta) \:\theta$
What is the Hessian of $f(\theta)$. In other words what is the derivative of $\nabla f(\theta)$.