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I know from definition that if some vector function $\mathbf{u}$ is given in three dimensional space, then curl is defined by this

$$\operatorname{curl}\mathbf{u}=\nabla\times \mathbf{u}=\left|\begin{matrix}\mathbf{i} & \mathbf{j} & \mathbf{k}\\ D_x & D_y & D_z\\ u_x & u_y & u_z\end{matrix}\right|$$

but unfortunately I forgot what represents subscript $D_x$. Is it the same as $u_x$? Because last one represents partial derivative and first one what is it?

Please help me.

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up vote 2 down vote accepted

$D_x=\frac{\partial}{\partial x}$ and similarly for $D_y$ and $D_z$. $u_x$ is the component of $u$ along $x$ and similarly for $u_y$ and $u_z$.

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