An equality about derivative of a polynomial?

[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?

 

[Mark44]

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?

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.