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Math Help - Leibnitz notation: treating it as a quotient

  1. #1
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    Leibnitz notation: treating it as a quotient

    Hi,

    How is it that you're allowed to treat the derivative dy/dx as an actual quotient, f.ex. when calculating in integral by substitution such as: integral f(x) dx, if you the y=f(x), and dy/dx = g(x), so that dx = dy/g(x) and so integral f(x) dx = integral y/g(x) dy.

    Clearly, we multiplied both sides of dy/dx = g(x) with dx! How is this possible? Isn't dy/dx just a notation denoting the derivative, not actual.... numbers?

    /Yair
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  2. #2
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    Re: Leibnitz notation: treating it as a quotient

    Quote Originally Posted by Yair1978 View Post
    Hi,

    How is it that you're allowed to treat the derivative dy/dx as an actual quotient, f.ex. when calculating in integral by substitution such as: integral f(x) dx, if you the y=f(x), and dy/dx = g(x), so that dx = dy/g(x) and so integral f(x) dx = integral y/g(x) dy.

    Clearly, we multiplied both sides of dy/dx = g(x) with dx! How is this possible? Isn't dy/dx just a notation denoting the derivative, not actual.... numbers?

    /Yair
    This will make an order in your thoughts: Differential of a function - Wikipedia, the free encyclopedia
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  3. #3
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    Re: Leibnitz notation: treating it as a quotient

    In fact, once you have defined "differentials", the fact that \frac{dy}{dx}= f(x) implies dy= f(x)dx is important in integration.
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