The Chain Rule & Implicit Differentiation · Medium problem

The temperature $T(x,y,z)$ has gradient $\nabla T(2,-1,3) = \langle 1, 4, -1\rangle$. A probe moves along $\mathbf r(t) = \langle 2t,\ -t^2,\ 3t^3\rangle$ and passes through $(2,-1,3)$ at $t = 1$. Find the rate of change of the temperature the probe records at $t = 1$.