From my matrix calculus books I understand that $\frac{d\textbf{u}(x)}{dx}$ is a column vector (I am using numerator layout here), where $\textbf{u}(x)$ is a column vector and $x$ is a scalar variable. However, what is the shape of the derivative if we are differentiating w.r.t a ROW vector? That is, what is the shape of $\frac{d(\textbf{u}(x))^T}{dx}$? Is it a row vector or column vector?
Also, is it true that $\frac{d\textbf{u(x)}}{d\textbf{x}}= \frac{d(\textbf{u}(\textbf{x}))^T}{d\textbf{x}}$? Here, the $\textbf{x}$ is a column vector but not a scalar.
Thank you very much!