Tutorial Exercise 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 = √10 + t, y = 7+1t, where x and y are measured in centimeters. The temperature function satisfies Tx(4, 8) = 4 and Ty(4, 8) : = 1. How fast is the temperature rising on the bug's path after 6 seconds? Step 1 dT We know that the rate of change of the temperature is given by dt aT dx ax dt aT dy + ay dt Using x = √10 + t and y = 7 + 1½t, we have dx dt and dy dt