\[\mathbf{T}_{u}=\frac{\partial x}{\partial u}(u_{0},v_{0})\mathbf{i}+\frac{%
\partial y}{\partial u}(u_{0},v_{0})\mathbf{j}+\frac{\partial z}{\partial u}(u%
_{0},v_{0})\mathbf{k}\]