Is it possible to get widely available math software (Maple/Matlab/Mathematica, etc) to symbolically differentiate vector and scalar functions of matrices, returning the result in terms of the original matrices and vectors involved? I have in mind the simple sort of rules collected [here](http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/IFEM.AppD.d/IFEM.AppD.pdf) for example.


On a few separate occasions I've scoured around the internet for such a thing and only turned up a bunch of incomplete threads of various vintage (like [this](http://www.varioustopics.com/math-symbolic/761236-vector-matrix-calculus-software.html) or [this](http://forums.wolfram.com/mathgroup/archive/2000/Feb/msg00451.html) or [this](http://forums.wolfram.com/mathgroup/archive/2001/Nov/msg00054.html)).


So my main question is if I am missing the right keywords to find what is obvious to people who use this sort of functionality all the time, and what platform it is available on if so. 


If in fact this sort of functionality is not available in any of the commonly used software my question is if this is because of some sort of practical obstruction I am not seeing or simply because the problems for which it would be useful are simple enough to be done by hand (which is what I've ended up doing after I spend 4 hours searching for the "easy" way).



Software for symbolic matrix calculus?
Indeed, I was having the same problem. Hence, I implemented a matrix calculus toolbox myself. You can find it at [www.matrixcalculus.org](http://www.matrixcalculus.org). It can compute vector and matrix derivatives and will return the result in terms of the original vectors and matrices involved.


