real analysis - Extension of Fundamental Theorem of Algebra

The problem states:

Let $p(x)$ be a polynomial in $x$ of degree $n$ with $n\ge2$. Recall that, according to the Fundamental Theorem of Algebra, $p(x)$ has $n$ number of roots in the complex number set. Suppose all roots of $p(x)$ are real and distinct. Prove that the roots of $p'(x)$ are all real.

I know and kind of understand the proof of the Fundamental Theorem of Algebra, but I do not know how to extend it to $p'(x)$. Any thoughts?

Thanks!