The teach gave us this question. We had to try to find the derivative of f(x) g(x).
multiplying the derivatives didn't give us the right answer. so we had to find a new way of find derivatives. We learned of 2 ways, that revolve around this formula.
This next slide is the classic formula. The basis of this formula is that you add and subtract same number so its like adding a zero.
After you add the "zero" you want to write out the whole equation.
You want to single out f(x+h) and g(x)
You the want to find n as it goes to zero for each part of the equation. And as n goes to Zero the equation g(x+h)- g(x) is the same as g'(x). Rewriting the equation by putting in g'(x) and f'(x) gives you your formula.
Sorry if its not that clear. Now the second way of doing it is the non traditional proof. Basically you can think of it as two rectangles. And all your doing is finding the difference between them. Take the differences, add them up and divide all that by h as h goes to zero. Remember that since h will be zero anything times to h will also be zero so therefore g'(x) f'(x) times h will be zero.
This is the whole procedure, have fun with it.
Now we had to do this all over again except this time with dividing. 
As you can see we once again need a new formula.but this time there is only one.
There is the the method of doing that and to end class we did a question(below).
I know this is not the best, but its all you will get for now. :) The next scribe will be........Robert? i can't tell who's done it or not by the scribe list.
Oh yea before I forget here is one of the sites the teach used in class. I managed to copy it down.
And lets not forget the little ditty we learned.
low de high minus high de low, all over low low :) have fun with it.
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