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An equality about derivative of a polynomial?

  1. Sep 30, 2015 #1

    td21

    User Avatar
    Gold Member

    Why is $$
    \left(x^2-1\right)\frac{d}{dx}\left(x^2-1\right)^n = 2nx\left(x^2-1\right)^{n-1}
    $$? This is in a textbook and says that its proof is left as an exercise. It seems to be a difficult equality.

    I believe this should just be $$
    \left(x^2-1\right)\frac{d}{dx}\left(x^2-1\right)^n = 2nx\left(x^2-1\right)^{n}
    $$ by simple differentiation.

    Am I wrong or not?
     
  2. jcsd
  3. Sep 30, 2015 #2

    Mark44

    Staff: Mentor

    What you have seems fine to me, but I can't say that the book is wrong without actually seeing what is in the book.
     
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