(Solved): The temperature at a point (x,y) is T(x,y), measured in degrees Celsius. A bug crawls so that its p ...

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 $$x=\sqrt{3+t},y=9+\frac{1}{6}t$$, where $$x$$ and $$y$$ are measured in centimeters. The temperature function satisfies $$T_x(3,10)=3$$ and $$T_y(3,10)=7$$. How fast is the temperature rising on the bug's path after 6 seconds? (Round your answer to two decimal places.) $${}^{?}\mathrm{C}/\mathrm{s}$$