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Math Help - Derivative

  1. #1
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    Question Derivative

    How do i find the derivitive with respect to x of:
    w = (x^2)+(y/x)

    AND with respect to y of the same equation.

    So in other words dw/dx and dw/dy?

    am confused how to differentiate y/x?

    Thanks
    Last edited by taurus; June 6th 2008 at 05:05 AM.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by taurus View Post
    How do i find the derivitive with respect to x of:
    w = (x^2)+(y/x)

    AND with respect to y of the same equation.

    So in other words dw/dx and dw/dy?

    am confused how to differentiate y/x?

    Thanks
    When you are differentiating in respect to a certain variable you treat the ohter variables as constants

    \therefore\frac{dW}{dx}=2x-\frac{y}{x^2}

    Can you go from there?
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  3. #3
    Lord of certain Rings
    Isomorphism's Avatar
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    Quote Originally Posted by taurus View Post
    How do i find the derivitive with respect to x of:
    w = (x^2)+(y/x)

    AND with respect to y of the same equation.

    So in other words dw/dx and dw/dy?

    am confused how to differentiate y/x?

    Thanks
    For all we know y might depend on x and thats why I think it is more complete to say,

    w = x^2+\frac{y}{x} \Rightarrow \frac{dw}{dx} = 2x + \frac1{x}\frac{dy}{dx} - \frac{y}{x^2}


    w = x^2+\frac{y}{x} \Rightarrow \frac{dw}{dy} = 2x \frac{dx}{dy} + \frac1{x} - \frac{y}{x^2}\frac{dx}{dy}
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