Consider the two-dimensional fluid flow represented by the Lagrangian transformation
\begin{equation} \vec{u} = \vec{X}(\vec{a}, \tau) = (a+\Gamma b \tau , b) \end{equation}
where $\vec{x} = (x,y), \vec{a} = (a,b) , \Gamma = constant$
Compute the Lagrangian velocity field:
\begin{equation} \vec{v}(\vec{a}, \tau) = \frac{\partial \vec{X}(a, \tau)}{\partial \tau} \end{equation}
This professor I have uses different mathematical notation that I am used to and for some reason this question is tripping me up when I feel like it is really easy