Given a real-valued function $f(x_1,x_2)$, we define the function $h(x_1,x_2) = |f(x_1,x_2)|^2$. I want to calculate the Hessian of $h$. Is the following expression correct?
\begin{align*} \frac{\partial^2 h}{\partial x_1 \partial x_2}=2 \frac{\partial f}{\partial x_1 } \frac{\partial f}{\partial x_2 } \end{align*}
If it is not true, in which condition, it can become true?