1. ## Chain rule

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 $x=\sqrt{1+t}, y=2+\frac{t}{3}$, where x and y are measured in centimeters. The temperature function satisfies Tx(2,3) = 4 and Ty(2,3)=3. How fast is the temperature rising on the bug’s path
after 3 seconds?

How can I begin with this?

Thank you.

2. Originally Posted by noppawit

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 $x=\sqrt{1+t}, y=2+\frac{t}{3}$, where x and y are measured in centimeters. The temperature function satisfies Tx(2,3) = 4 and Ty(2,3)=3. How fast is the temperature rising on the bug’s path
after 3 seconds?

How can I begin with this?

Thank you.
What you're going to need is

$\frac{dT}{dt} = T_x \frac{dx}{dt} + T_y \frac{dy}{dt}$