And in particular, let's see, I am going to factor out an f of x plus h. So if you factor out an f of x plus h, this part right over here is going to be f of x plus h, f of x plus h, times, you're going to be left with g of x plus h, g of, it's a slightly shader, different shade of green, g of x plus h, that's that there, minus g of x, minus g of x, whoops, I forgot the parentheses. Oh, it's a different color. I got a new software program and it's making it hard for me to change colors. My apologies, this is not a straightforward proof and the least I could do is change colors more smoothly. All right, g of x plus h, minus g of x, that's that one right over there, and then all of that over this h, all of that over h, so that's this part here, and then this part over here, this part over here, and actually it's still over h, so let me actually circle it like this. So, this part over here, I can write as, so then we're going to have plus, actually here let me, let me factor out a g of x here. So, plus g of x, plus g of x, times this f of x plus h, times f of x plus h, minus this f of x, minus that f of x, all of that over h, all of that over h. Now, we know from our limit properties, the limit of all of this business, well, that's just going to be the same thing as the limit of this as h approaches zero, plus the limit of this as h approaches zero, and then the limit of the product is going to be the same thing as the product of the limits.