$\frac{dAx}{dx’} = A$ 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?