Differentiation Involving Determinant.

#1
I have to compute the following differentiation :

[math]\frac{\partial}{\partial\sigma^2}\det[\mathbf X_{p\times n}'(\sigma^2 \mathbf I_{n}+\mathbf Z_{n\times q}\mathbf G_{q\times q}\mathbf Z_{q\times n}')^{-1}\mathbf X_{n\times p}],[/math]

where [math]\sigma^2[/math] is a scalar, [math]\det[/math] denotes determinant, [math]\mathbf I_{n}[/math] is a $n\times n$ identity matrix. Note that, [math]\mathbf X[/math], [math]\mathbf Z[/math], and [math]\mathbf G[/math] do NOT involve [math]\sigma^2[/math].

How can I do that?
 
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