I see two different formulae.

https://www.comp.nus.edu.sg/~cs5240/lecture/matrix-differentiation-c.pdf

In this slides page 9, the derivative of $Ax$ is $A$.

But in some other documents such as http://faculty.arts.ubc.ca/vmarmer/econ627/vector%20diff.pdf. The derivative is $A^T$.

How to properly evaluate the derivative of Ax?