How to calculate $\frac{\partial \mathbf{A}}{\partial \mathbf{x}}$?

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How to calculate $\frac{\partial \mathbf{A}}{\partial \mathbf{x}}$?

Here $\mathbf{A}$ is a matrix and $\mathbf{x}$ is a vector. Thank you very much.

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That is the Jacobian of a vector valued function. Unfortunately this popular notation is not very self explanatory.

See Jacobian