## Deriviative of the coherence matrix

Hi. First of all I don't know if this belongs in the Linear Algebra forum or the Calculus forum (its a bit of both!) so apologies for cross-posting!

I am trying to find analytical expression for the derivative of the coherence (or correlation) function of a matrix.

So M(C) is the coherence matrix of some positive-definite, symmetrical, real or complex, matrix C. such that:

$m_{ij}=c_{ij}/(c_{ii}c_{jj})^{1/2}$

Is it possible to get an analytical expression for $dM/dC$ ? I'm not sure how differentiation works for matrix functions which operate on different elements within the matrix.