Science:Math Exam Resources/Courses/MATH200/December 2011/Question 03 (b)/Hint 1

The rate of change of the temperature is the derivative of the temperature, which is the partial derivative of the temperature plus the directional derivative of $\displaystyle T$ in the direction of the velocity vector v of the bee,

${\frac {dT}{dt}}={\frac {\partial T}{\partial t}}+\nabla T\cdot \mathbf {v}$

The vector v for the time $t=2$ is already determined in part (a).