Ex 2: Related Rates: Determine the Rate of Change of the Area of a Circle With Respect to Time

This video provides an example of how to determine how fast the area of circular sheet of ice is shrinking.

[Sean-eszc]

Dear sir, thank you so much for the wonderful tutorial from Hong Kong!
I have 2 questions regarding this type of problem relating to derivative of circle, that is
1. why does product rule: d/dx (uv) = u dv/dx + v du/dx, not apply to the case of derivative of πr^2? (but only power rule is applied to turn the power of r into coefficient of the whole equation.)
2. if the product rule does not apply, why is the derivative of π (a component in πr^2) not equal to 0 given it is real number?

Thank you very much, would really appreciate if you could let me know if there are any wrong presumptions of my understanding towards derivative rule in these 2 questions, these have been bugging me across 2 semesters 🙏😭