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Math Help - Implicit Differentiation

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    Junior Member Greymalkin's Avatar
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    Implicit Differentiation

    Im trying to find tangency points in a problem so I need to differentiate, x^2+y^2=4000^2

    Why is the derivative of y2=0? I thought by the laws of implicit differentiation that you just multiply the y term by its derivative which then follows the same rules as x does, so using the power rule would result with y2=2y. Why does y2=0 then when I plugin the formula into wolfram?
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    Re: Implicit Differentiation

    Quote Originally Posted by Greymalkin View Post
    Im trying to find tangency points in a problem so I need to differentiate, x^2+y^2=4000^2
    The derivative is y'=\frac{-x}{y}~.
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    Re: Implicit Differentiation

    Quote Originally Posted by Greymalkin View Post
    Im trying to find tangency points in a problem so I need to differentiate, x^2+y^2=4000^2

    Why is the derivative of y2=0? I thought by the laws of implicit differentiation that you just multiply the y term by its derivative which then follows the same rules as x does, so using the power rule would result with y2=2y. Why does y2=0 then when I plugin the formula into wolfram?
    Wolfram is evaluating a PARTIAL derivative with respect to x. This is not what you want.
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    Junior Member Greymalkin's Avatar
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    Re: Implicit Differentiation

    Quote Originally Posted by Plato View Post
    The derivative is y'=\frac{-x}{y}~.
    My answer was:
    x^2+y^2=4000^2
    2x+y^2(y')=0
    so I get y'=\frac{-2x}{y^2} how is it you arrived at your answer? I doesn't really matter much anyways because the answer to my problem used the derivative in the form of y=\sqrt{4000^2-x^2} anyways. I think you are dividing by 2y instead of y2, How is that a derivative when it is y2=?
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    Re: Implicit Differentiation

    Quote Originally Posted by Greymalkin View Post
    My answer was:
    x^2+y^2=4000^2
    2x+y^2(y')=0
    It should be 2x+2(y)y'=0
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