# velocity gradient in cylindrical coordinate.

In cartesian co-ordinate ($$x,y,z$$), gradient of velocity($$\mathbf{u}=(u_x,u_y,u_z)$$)(Jacobian matrix)is defined: $$\begin{equation*} \nabla \mathbf{u}= \begin{pmatrix} \partial_x u_x && \partial_y u_x&&\partial_z u_x \\ \partial_x u_y && \partial_y u_y&&\partial_z u_y \\ \partial_x u_z && \partial_y u_z&&\partial_z u_z \end{pmatrix} \end{equation*}$$ Then what is the gradient of velocity ($$\mathbf{u}=(u_r,u_\theta,u_z)$$), in cylindrical coordinate($$r,\theta,z$$)? and how we derive that?