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Math Help - Problem understanding last part of product rule proof

  1. #1
    Senior Member Paze's Avatar
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    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.
    Last edited by Paze; February 4th 2013 at 09:01 PM.
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  2. #2
    MHF Contributor
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    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.
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  3. #3
    Senior Member Paze's Avatar
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    Re: Problem understanding last part of product rule proof

    Quote Originally Posted by chiro View Post
    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..
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