Wikipedia says that given $f(x) = x^TA$: $$\frac{\partial f}{\partial x} = A^T$$
but I am having trouble understanding this result. I tried doing the following:
$$f(x+h) - f(x) = h^TA$$
I am now stuck at making the above expression into a linear mapping of $h$. I'm not sure how to relate this to $A^T$. If $A$ were a vector, it would be easy because I could just switch the transpose and have $h^Ta = a^Th$. Since $A$ is a matrix, I am not sure how to proceed.