# Thread: Derivative function as a periodic function but primitive function not periodic one

1. ## Derivative function as a periodic function but primitive function not periodic one

Hi,

I have a problem to figure out an example of primitive (antiderivative) function (as much simple as possible) which is NOT periodic function that is f(x+T)!=f(x) (where T is a period)
but it's derivative IS a periodic one.
I can proof the opposite case (use definition of derivative) if f(x) is periodic then it's derivative is also periodic, but according to a book which I'm studing now,
the opposite direction need not be true.

Thanks for help,

jeel

2. ## Re: Derivative function as a periodic function but primitive function not periodic on

What about sin(x) + 1?

3. ## Re: Derivative function as a periodic function but primitive function not periodic on

Thanks, sometimes the simplest things are the hardest to grasp, of course definitely this is such kind of a function.

emakarov, thank you very much !!!

### derivative periodic then function

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