Hi,everyone,I got a problem here that I don't understand.Can anyone please help me?
The relation between three-dimentional cartesian coordinates and cylindrical coordinates is given by
Calculate the partial derivatives , and in terms of , , .
My current problem here is like a puzzle. I certainly can solve the question and find the answer. For example, I did find .Same as solution
However, my problem occured when I want to calculate ,if I just use , I would get as well!
I think it is weird, because I thought supposed to equal to the reciprocal of , which means it supposed to be .
So pretty sure is the right answer(same as solution),but why the recipocal rule does not apply here? I'm so confused about this puzzle. Same as two other questions.(Headbang)
What was your process by which you obtained
Oddly enough, both and are correct.
Your "mistake" is in thinking that and must be reciprocals. For partial derivatives, that simply is not true.
Thanks a lot.
Originally Posted by HallsofIvy
I felt the reason must be because their are partial derivatives, therefore they are not reciprocals.
But I wonder the reason, is there any mathematical way can explain that? Thanks a lot.