I'm trying to figure out how to compute derivatives for the following:
Consider
\begin{equation} \left[ N^{-1} Z' \left( y - X \beta \right) \right]^{'} W_N \left[ N^{-1} Z' \left( y - X \beta \right) \right] \end{equation}
where $N$ is a scalar, $Z$ is an $N \times L$ matrix, $X$ is an $N \times K$ matrix, with $L \ge K$, $y$ is a column vector of size $n$ and $W_N$ is an $L \times L$ positive definite symmetric matrix.
I should differentiate with respect to $\beta$ and get
\begin{equation} \beta = (X'ZW_NZ'X)^{-1} X'ZW_N Z'y \end{equation}
Can you kindly spell out the steps to get $\beta$?