# I don't understand operators

So I was reading from my quantum book (Gasiorowicz) and I ame across this sentence:

$$[p^2, x] = p [p, x] + [p, x] p = \frac{2\hbar}{i} p$$

I don't understand this. I know that $$p = -i \hbar \frac{\partial}{\partial x}$$, but I can't see how to get that expression...I just come up with something like $$x {\hbar}^2 \frac{{\partial}^2}{{\partial x}^2}$$ when I try multiplying it out.

try to derive $$[AB,C] = ?$$
then use $$[x,p] = i\hbar$$
to find $$[p^2,x]$$

nrqed
$$[p^2, x] = p [p, x] + [p, x] p = \frac{2\hbar}{i} p$$
I don't understand this. I know that $$p = -i \hbar \frac{\partial}{\partial x}$$, but I can't see how to get that expression...I just come up with something like $$x {\hbar}^2 \frac{{\partial}^2}{{\partial x}^2}$$ when I try multiplying it out.
$$[x,p_x] f(x) = -i \hbar x \partial_x f(x) + i \hbar \partial_x (x f(x))$$ apply the product rule on the second term and then something will cancel out. At the very end of the calculation (and only then) you may drop the test function f(x).