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Math Help - I don't understand differentials..dy and dx terms ect.

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    I don't understand differentials..dy and dx terms ect.

    I know that dy/dx is the notation for the derivative of a function and i also know that dy is the infinitely small difference between two y values and dx is the infinitely small difference between two x values.

    The part that confuses me is when i see the dy and dx seperated from eachother on both sides of an equation. I don't know what that means.
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  2. #2
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    Doesn't mean much unless you are solving a separable differential equation. You can always use the rules of algebra to put them together whether you divide or multiple them across.
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    Quote Originally Posted by jsel21 View Post
    I know that dy/dx is the notation for the derivative of a function and i also know that dy is the infinitely small difference between two y values and dx is the infinitely small difference between two x values.

    The part that confuses me is when i see the dy and dx seperated from eachother on both sides of an equation. I don't know what that means.
    Let say we have a function such as this:

    \frac{dy}{dx} = \frac{F(x)}{G(y)}.

    If you treat \frac{dy}{dx} as a simple fraction, you can "multiply" in a sense by dx and rearrange to get.

    G(y)dy = F(x)dx, and integrate both sides with respect to the respective variables.

    As dwsmith said this is used when solving separable differential equations.
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    ok, another thing i don't understand is the meaning of differentiating "y in respect to x", or differentiating y in respect to any other variable. what exactly does it mean to differentiate y "in respect to" a variable?
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    Quote Originally Posted by jsel21 View Post
    ok, another thing i don't understand is the meaning of differentiating "y in respect to x", or differentiating y in respect to any other variable. what exactly does it mean to differentiate y "in respect to" a variable?
    Try reading it as "as it depends on" or "as it varies with".

    E.g. speed is the rate of displacement of an object with respect to (depending on) time.
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