# derivative of a matrix inverse

I wonder how to differentiate with respect to the diagonal matrix $X_d$, the following matrix :

$$X_d^T (\Sigma_d + X_d C X_d)^{-1} X_d$$

where $X_d$ and $\Sigma_d$ are diagonal matrices with striclty positive diagonal entries and $C$ is a positive definite matrix. Any hint would be appreciated.

• How to derive this from what? What do each of the terms represent? – Tom Jun 4 '14 at 13:41
• @Tom. Does the edit help ? Thanks. – peuhp Jun 4 '14 at 13:47