What area of mathematics would handle matrix differentiation?

∂/∂x( x A T + (A xT + (xT A−1 x)(xT y))

Ts are the transposes and -1 are the inverses.

I understand partial differentiation wrt a variable.

I understand the matrix algebra of multiplying x by the transpose of a matrix.

I found some matrix identities but they don't help me understand why. Just need a place to start.

Thanks for any help.

That's a good book, but...

Right, but what I need is to find out what rules apply to that differentiation.