How to get the Hessian Matrix please?

I have got the following function constructed by matrices and vectors:

$\displaystyle

f(x, \alpha) = \frac{1}{2}[(Ax-y_1)^2+(AP(\alpha)x-y_2)^2]

$

in which, $\displaystyle x, y_1, y_2$ are vectors. $\displaystyle A, P(\alpha)$ are matrices.

The gradients with respect to $\displaystyle x, \alpha$ are:

$\displaystyle

\frac{\partial{f(x, \alpha)}}{\partial{x}} = A^T A x - A^T y_1 + P(\alpha)^T A^T A P(\alpha) x - P(\alpha)^T A^T y_2

$

$\displaystyle

\frac{\partial{f(x, \alpha)}}{\partial{\alpha}} = x^T P(\alpha)^T A^T A P(\alpha) x - x^T P'(\alpha)^T A^T y_2

$

in which, $\displaystyle A^T$ is the transpose of $\displaystyle A$ and $\displaystyle P'(\alpha)$ is the first order derivative of $\displaystyle P$.

Anyone knows how to get the Hessian of the $\displaystyle f(x, \alpha)$? Thanks a lot! (Happy)