So I'm having a bit of trouble here...

I want to prove the product rule:

So assuming that f and g are differentiable at Xo:

And in the same way, with some rearrangement.

And, obviously:

Substituting equations 1 and 2 and multiplying out yields:

So now the example I'm following just leaves things here, so apparently this is enough, but I don't see how this simplifies to what I understand to be the goal of the exercise i.e.

Thanks in advance.