- #1
AlexChandler
- 283
- 0
I have come to a bit of a misunderstanding with partial derivatives. I will try to illustrate my problem. Say we have a function f(x, y(x), y'(x)) where y'(x)=dy/dx. Now suppose that f does not explicitly depend on x. My physics book says at this point that ∂f/∂x=0, even though y(x) and y'(x) may depend on x.
Suppose f=y2
Then ∂f/∂x=0
but if we have y(x)=x, then we can write f as:
f=x2 and we have
∂f/∂x=2x
How can we have two different answers for the same derivative by simply rewriting the function in a different way?
I apologize in advance if the answer is obvious and I am being a bit annoying by asking. But if you do have a helpful comment to post, I would greatly appreciate it!
-Alex
Suppose f=y2
Then ∂f/∂x=0
but if we have y(x)=x, then we can write f as:
f=x2 and we have
∂f/∂x=2x
How can we have two different answers for the same derivative by simply rewriting the function in a different way?
I apologize in advance if the answer is obvious and I am being a bit annoying by asking. But if you do have a helpful comment to post, I would greatly appreciate it!
-Alex