# Periodic Function: Derivative & Integral

• buzzmath
In summary, a periodic function is a mathematical function that repeats its values at regular intervals. The derivative of a periodic function represents the rate of change of the original function at any given point and can be found using standard rules of differentiation. The integral of a periodic function is the inverse operation of differentiation and can be calculated using the fundamental theorem of calculus, resulting in a periodic 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.

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.

## 1. What is a periodic function?

A periodic function is a mathematical function that repeats its values at regular intervals. This means that the function will have the same values at specific points on its graph, known as periods.

## 2. What is the derivative of a periodic function?

The derivative of a periodic function is a new function that represents the rate of change of the original function at any given point. In other words, it tells us how the value of the function is changing at a specific point.

## 3. How do you find the derivative of a periodic function?

To find the derivative of a periodic function, you can use the standard rules of differentiation, such as the power rule, product rule, and chain rule. However, since the function repeats itself, the derivative will also repeat itself, resulting in a periodic function.

## 4. What is the integral of a periodic function?

The integral of a periodic function is the inverse operation of differentiation. It represents the area under the curve of the function and can be used to find the total change or accumulation of the function over a given interval.

## 5. How do you calculate the integral of a periodic function?

To calculate the integral of a periodic function, you can use the fundamental theorem of calculus, which states that the integral of a function can be found by evaluating the antiderivative of that function at the upper and lower bounds of the integral. For a periodic function, this will result in a periodic integral as well.

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