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 that I just couldn't figure out for 2 semesters 🙏😭
Welcome to the channel! 1) The product rule is only used when there is a product of VARIABLE (Like xy) In this case pi is a number not a variable, therefore the product rule is not used. 2) d/dr ( pi r^2) = pi d/dr( r^2) = pi ( 2 r) = 2 pi r
These example videos are great. Always a good feeling to get it right and if one makes a mistake the explanation is just a click away :)
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 that I just couldn't figure out for 2 semesters 🙏😭
Welcome to the channel! 1) The product rule is only used when there is a product of VARIABLE (Like xy) In this case pi is a number not a variable, therefore the product rule is not used. 2) d/dr ( pi r^2) = pi d/dr( r^2) = pi ( 2 r) = 2 pi r
@@MichelvanBiezen Dear sir, thank you very much! Those are some really clear explanations!
Another interesting video. Thanks.
I would never have thought to use d=vt.
I have a Calc exam coming up and rn youre saving my ass
All the best on your exam.
Thanks, Sir!
Most welcome!
I thought pi is a constant? Wouldn’t its derivative be zero?
pi is a constant. But it is the numerical coefficient of R which is a variable.
If it was ....+Pi then it would go when differentiated since it’s a constant
How wouldve taking a derivative of the third variable looked like if i had used: (f(x+h)-f(x))/h
Wouldn’t the diameter be 20?
No, the radius would be 20 feet. 2 ft/sec x 10 sec = 20 feet and the ripples move away from the center
Thanks ^_^
You're welcome!