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Thread: Fundamental question: we know that y = x dy/dx, or rather... y/x = dy/dx...

  1. #1

    Fundamental question: we know that y = x dy/dx, or rather... y/x = dy/dx...

    I'm confused:
    we know that y = x dy/dx, or rather... y/x = dy/dx,
    suppose y = x^2,
    dy/dx = 2x
    y/x = 2x
    y = (2x)x
    y = 2x^2 ? contradiction?

  2. #2
    Elite Member
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    Quote Originally Posted by dinomight View Post
    I'm confused:
    we know that y = x dy/dx, or rather... y/x = dy/dx,
    suppose y = x^2,
    dy/dx = 2x
    y/x = 2x
    y = (2x)x
    y = 2x^2 ? contradiction?
    Yes it is contradiction - and it says that:

    y =x^2

    is NOT a solution for:

    y = x dy/dx ..... !
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by dinomight View Post
    I'm confused:
    we know that y = x dy/dx, or rather... y/x = dy/dx,...
    Are you saying that you think this equality is true for all x and y?

  4. #4
    Senior Member
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    Quote Originally Posted by stapel View Post
    Are you saying that you think this equality is true for all x and y?
    I think that the OP is saying just that. (To OP) Why do you think that equation is always true (called an identity)? YOU even found a counter example! You are thinking that y=dy and x=dx? If if y=x^2, then to compute the derivative, dy/dx, you just divide both sides by x? So there is no need to ever use the product rule, the quotient rule nor the chain rule since you can just divide by x? Please think about what I am saying!
    Last edited by Jomo; 06-17-2017 at 12:01 PM.
    A mathematician is a blind man in a dark room looking for a black cat which isn’t there. - Charles R. Darwin

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