# Problem understanding last part of product rule proof

• Feb 4th 2013, 06:39 PM
Paze
Problem understanding last part of product rule proof
Hi. I'm having a problem why v(x+deltaX) and u(x) become V and U respectively.

The problem is highlighted in my calculations:

http://s7.postimage.org/gqdjxm263/MITprodprood.png

Thanks you very much!

I should probably note that the problem ends as the definition: $\frac{du}{dx}\cdot v+u\cdot \frac{dv}{dx}$

And I don't understand how they become V and U in the end.

Bonus question: The teacher keeps saying that for example in the quotient rule proof that v(v+deltaV) becomes v^2 because "they are continuous". I just can't get that part either. Thanks.
• Feb 4th 2013, 09:07 PM
chiro
Re: Problem understanding last part of product rule proof
Hey Paze.

It follows directly from the line above: the only difference in the two lines is that the whole thing is now divided by the delta_x (triangle x) term.
• Feb 5th 2013, 07:42 AM
Paze
Re: Problem understanding last part of product rule proof
Quote:

Originally Posted by chiro
Hey Paze.

It follows directly from the line above: the only difference in the two lines is that the whole thing is now divided by the delta_x (triangle x) term.

I still don't understand. It's not supposed to say VX like on my picture, it's supposed to say just V. Which is what baffles me. Also U(x) magically becomes U..