So . Now, what is your question?
Suppose the temperature are point in space is
Let a particle follow the right circular helix and let be its temperature at time t
a) what is
theres a part (b) but I'll wait till I get this part
I think you have the wrong formula for the derivative of T with respect to t. If x, y, and z were measured in metres and t in seconds then dT/dt in your formula would have units of metres squared per second squared
To my knowledge the total derivative is