## $\frac{dAx}{dx’} = A$ makes sense as Ax becomes a column vector given x is a column vector, but I see elsewhere $dAx/x=A$

$$\frac{d\bf{Ax}}{d\bf{x}’} = \bf{A}$$ makes sense as $$\bf{Ax}$$ becomes a column vector given $$\bf{x}$$ is a column vector and $$\bf{A}$$ is a $$n\times n$$ matrix, but I see elsewhere that states $$\frac{d\bf{Ax}}{d\bf{x}} = \bf{A}’$$, which doesn’t makes sense (to me!) because it takes a derivative of $$\bf{Ax}$$ by the column vector which should place each partial column-wise. What is the explanation of this result?