An insect is moving on the ellipse $2x^2 + y^2 = 3$ on the xy-plane in the clockwise direction at a constant speed of 3 centimeter per second. The temperature function $T(x; y)$ (experienced by the insect) is given by $T(x , y) = 3x^2 - 2yx$; where $T$ is measured in degree Celsius and x, y are measured in centimeters. What is the rate of change of the temperature (in degree Celsius per second) when the insect is at the point $(1, 1)$? Hint: Let $f(x; y) = 2x^2 + y^2$. The gradient vector Of(1,1) = <4, 2> is normal to the ellipse $f(x, y) = 3$ at the point $(1, 1)$. Using this information, how can we easily find a vector which is tangential to the ellipse $f(x, y) = 3$ and is pointing in the clockwise direction?
Anyone please help solving this question! Even with the hint dropped by the lecturer, I still cannot get it!