Periodic Function: Derivative & Integral

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Homework Statement


Is the derivative of a periodic function periodic?
Is the integral of a periocic function periodic?

Homework Equations



a function if periodic if f(x)=f(x+p)

The Attempt at a Solution



I think that the derivative won't be periodic but the integral will. I'm not really sure if I'm right or not though.
 
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If this is an opinion poll, I think the opposite is true. Spell out why you think so and we can compare opinions. Try sin(x)+1.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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