Section 14.5 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 \(x = \sqrt{1 + t}\), \(y = 2 + \frac{1}{3}t\), where \(x\) and \(y\) are measured in centimeters. The temperature function satisfies \(T_x(2, 3) = 4\) and \(T_y(2, 3) = 3\). How fast is the temperature rising on the bug’s path after 3 seconds?