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

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

    Quote Originally Posted by Mathinik View Post
    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?
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    Re: When taking multiple derivatives of a polynomial, will there ever be an end?

    Quote Originally Posted by Mathinik View Post
    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.
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    Re: When taking multiple derivatives of a polynomial, will there ever be an end?

    Quote Originally Posted by Prove It View Post
    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!
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