# Thread: When taking multiple derivatives of a polynomial, will there ever be an end?

1. ## When taking multiple derivatives of a polynomial, will there ever be an end?

When taking multiple derivatives of a polynomial, will there ever be an end?

2. ## Re: When taking multiple derivatives of a polynomial, will there ever be an end?

Originally Posted by Mathinik
When taking multiple derivatives of a polynomial, will there ever be an end?
Polynomials are defined as functions that are made entirely of terms like \displaystyle \begin{align*} a\, x^n \end{align*} where \displaystyle \begin{align*} n \end{align*} can only take on nonnegative integer values. What happens to terms that look like this when you differentiate?

3. ## Re: When taking multiple derivatives of a polynomial, will there ever be an end?

Originally Posted by Mathinik
When taking multiple derivatives of a polynomial, will there ever be an end?
If by end you mean you will get the zero function. The answer is yes. If you take n+1 derivatives of an nth degree polynomial you will always get zero.

4. ## Re: When taking multiple derivatives of a polynomial, will there ever be an end?

Originally Posted by Prove It
Polynomials are defined as functions that are made entirely of terms like \displaystyle \begin{align*} a\, x^n \end{align*} where \displaystyle \begin{align*} n \end{align*} can only take on nonnegative integer values. What happens to terms that look like this when you differentiate?

becomes constant and then 0 then it's over, got it ty!