Hi I have a small doubt on Discrete Geometry, more specifically the derivation of Jacobian.
Say we have a function $x:\mathbb{R}^2\supseteq U \rightarrow \mathbb{R}^3 : (u,v) \mapsto x(u,v)$
Also now we have a parametric curve defined as $ \gamma(t) = x(u_0 + tw_1,v_0+tw_2)$
Then in the text I am referring to, it is written that $\gamma'(0)=w_1x_u + w_2x_v$
where $ x_u = {\delta x \over \delta u}$ and $x_v = {\delta x \over \delta v} $
My question is how is this formula for $ \gamma'(0) $ arrived at? I am sure its some elementary maths which I am missing out. Also if you need more information please ask for the same.