Consider, $i$ and $j$ are unit vectors along $x$ and $y$ directions of a Cartesian $(x, y)$ coordinate system, respectively and $t$ is time. Temperature ($T$) and fluid velocity $(\vec{V})$ are given for a flow field as:
$$\begin{array}{l} T=x^{2}+y t+35 \\ \vec{V}=(4 x y) i+\left(x t-2 y^{2}\right) j \end{array} $$
The total rate of change of temperature in the flow field (in integer) for time $t=2$ at a point $(2,3)$ is $\_\_\_\_\_\_$
