Transforming a multivariate normal

Question

I don't understand where the part underlined in green comes from.

Answer 1

$$ \mathbf{X} = \mathbf{M}^{-1}\mathbf{Y} $$ Such that $$ x_{i} = c_{ij}y_{j} $$ Here $c_{ij} = [\mathbf{M}^{-1}]_{ij}$. So now you can see where the derivative comes from?