Determine the derivative of $(x^2-1)^{50}$.

We see that this is of the form $[f(x)]^n$ where $f(x)=x^2-1$ and $n=50$. So from the Chain Rule we know that \[\frac{d}{dx}\left[\,[f(x)]^n\,\right]=n\left[\,f(x)\,\right]^{n-1}\cdot\frac{df}{dx}.\] Since $f'(x)=2x$ we see that
\[
\frac{d}{dx}\left[(x^2-1)^{50}\right]=50(x^2-1)^{49}\cdot 2x=100x(x^2-1)^{49}.
\]