1. ## Derivative

Hi,

I have a question:

I have the function :
f(x)=(X^(2n))*sin(1/x) when x is no 0, and f(x)=0 when x=0.
the question is how many times we can Derivative f(x) in x=0.

thanks to anyone that can help!

2. If both right and left limits (falling and rising to 0, respectively) of f(x) exist (and are same), then you can take derivative (you can differentiate) of f(x) at x=0, unlimited times.

3. hi,

how do you proof this??