The $T(x, y)$ (in degrees Celsius) at a point $(x, y)$ in a metal plate is given by:
$$T(x,y) = 100e^{-x^2-y^2}$$
If a small insect is moving in the direction of increasing $x$ at the point $(1, 1)$, what is the rate of temperature change in that direction? Show all your work.
(This problem models heat distribution in a metal plate, where partial derivatives represent how temperature varies in different directions.)
