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. So, if I use both of those limit properties, I can rewrite this whole thing as the limit, let me give myself some real estate, the limit as h approaches zero of f of x plus h, of f of x plus h, times, times the limit as h approaches zero of all of this business, g of x plus h, minus g of x, minus g of x, all of that over h, I think you might see where this is going, very exciting, all right, plus, plus the limit, let me write that a little bit more clearly, plus the limit as h approaches zero of g of x, our nice brown colored g of x, times, now we're going to have a product here, the limit, the limit as h approaches zero of f of x plus h, of f of x plus h, minus f of x, minus f of x, all of that, all of that over h, and let me put the parentheses where they're appropriate, so that, that, that, that, and all I did here, the limit, the limit of this sum, that's going to be the sum of the limits, that's going to be the limit of this, plus the limit of that, and then the limit of the products is going to be the same thing as the product of the limits, so I just use those limit properties here, but now let's evaluate them. What's the limit, and I'll do it in different colors, what's this thing right over here? The limit as h approaches zero of f of x plus h, well that's just going to be f of x.