Question

The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by
x =sqrt(1 + t), y = 2 +(1/3)t,
where x and y are measured in centimeters. The temperature function satisfies Tx(2, 3) = 3
and Ty(2, 3) = 3.
How fast is the temperature rising on the bug's path after 3 seconds?

Answer 1

\[\frac{\partial T}{\partial t}=\frac{\partial T}{\partial x}\frac{dx}{dt}+\frac{\partial T}{\partial y}\frac{dy}{dt}\]
Use this formula. It's the Chain Rule for multiple variables.

Answer 2

Yeah, I got it a while ago. Thanks though. Forgot to close the question.