Variance of $\beta$ in Quasi-likelihood Function

Question

We know that the Quasi-likelihood function is $$ U(\beta) = D^{T} V^{-} [Y - \mu(\beta)], $$ where D is a $n \times p$ matrix with elements $\frac{\partial \mu_i(\beta)}{\partial \beta_j}$, $V^{-}$ is a $n \times n$ generalized inverse matrix, Y is a $n \times 1$ vector, and $\mu(\beta)$ is also a $n \times 1$ vector. I know that the variance of estimated $\beta$ from Quasi-likelihood function is $$ Var(\hat{\beta}) = \sigma^2 D^{T} V^{-} D $$ and it should be the negative expectation of $U(\beta)$, but I can not figure out the detail of the matrix derivative. That is $$ \frac{\partial U(\beta)}{\partial \beta} = \frac{\partial}{\partial \beta} D^{T} V^{-} Y - \frac{\partial}{\partial \beta} D^{T}V^{-} \mu(\beta). $$ I am wondering how can I obtain the form of $Var(\hat{\beta})$ via the derivative?