if a differentiable function f:R to R is periodic then f'(x) is also periodic.is it true or not

Question

anonymous · Answer

Well take a periodic function. Cos x 

The derivative of cosx is -sinx. Sinx x is still periodic.

anonymous · Answer

thank you but if it is true a need a proof. an example is not enough

anonymous · Answer

Yeah I know I was going to say if you truly want to understand why this is true then you have to find the proof of why f(x)=cos x and f'(x)- - sin x

But I'm really bad at explaining those proofs.

accessdenied · Answer

I think if we use the fact that f(x) is periodic if there is a constant T such that f(x + T) = f(x), then we can take the derivative of both sides to show that f'(x+T) = f'(x).

As I think about it intuitively, the slope at each point should technically be the same if its just the same graph repeating itself...

accessdenied · Answer

By that ' the slope at each point... be the same', I mean the same point on each repetition of the graph.

anonymous · Answer

thank you

accessdenied · Answer

You're welcome.  :)