- #1
Hertz
- 180
- 8
The problem I'm curious about is this:
[itex]\frac{\partial}{\partial r}(\frac{\partial r}{\partial θ})[/itex]
I found that the answer is zero using WolframAlpha, but obviously I won't have that on a future test xD. Can someone please explain to me how to think about the derivative above? How can I look at it and intuitively say "Oh, that derivative is equal to zero!"
-edit
I do see that [itex]\frac{\partial r}{\partial \theta}[/itex] is usually only a function of theta, so therefore the partial with respect to r would be zero. But when you differentiate implicitly you can get r' in terms of both r and θ right?
[itex]\frac{\partial}{\partial r}(\frac{\partial r}{\partial θ})[/itex]
I found that the answer is zero using WolframAlpha, but obviously I won't have that on a future test xD. Can someone please explain to me how to think about the derivative above? How can I look at it and intuitively say "Oh, that derivative is equal to zero!"
-edit
I do see that [itex]\frac{\partial r}{\partial \theta}[/itex] is usually only a function of theta, so therefore the partial with respect to r would be zero. But when you differentiate implicitly you can get r' in terms of both r and θ right?