# An equality about derivative of a polynomial?

1. Sep 30, 2015

### td21

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. Sep 30, 2015

### 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.