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Math Help - Implicit differentiation

  1. #1
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    Implicit differentiation

    Here my question , for example x^2*y^2=0 when y=x=1, find d/dx, can I make the y^2 = x^2 and therefor change the equation to x^4=0 and differentiate for my x?
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  2. #2
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    Re: Implicit differentiation

    Quote Originally Posted by Frozenboy11 View Post
    Here my question , for example x^2*y^2=0 when y=x=1, find d/dx, can I make the y^2 = x^2 and therefor change the equation to x^4=0 and differentiate for my x?
    That is an impossible example.
     x^2y^2=0 when  y=x=1 does not exist.
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    Re: Implicit differentiation

    Ok my bad let said it is equal to some number so can I let y^2=x^2? When x=y=1?
    Last edited by Frozenboy11; November 14th 2012 at 07:08 AM.
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    Re: Implicit differentiation

    Quote Originally Posted by Frozenboy11 View Post
    Ok my bad let said it is equal to some number so can I let y^2=x^2? When x=y=1?
    If y^2=x^2 then 2yy^{\prime}=2x or y^{\prime}=\frac{x}{y}.

    SO?
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    Re: Implicit differentiation

    Quote Originally Posted by Plato View Post
    If y^2=x^2 then 2yy^{\prime}=2x or y^{\prime}=\frac{x}{y}.

    SO?
    Here the full question
    Last edited by Frozenboy11; November 14th 2012 at 08:40 AM.
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  6. #6
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    Re: Implicit differentiation

    Yes, that is wrong. "At x= y= 1" does not mean that you can set x= y before taking the derivative. You have to take the derivative, with respect to y as (1, y) approaches (1, 1). So, because this is the partial derivative with respect to 1, you can set x= 1, making f(x, y)= ln((1+2y)^2+ (2- y)^2+ 4y^2). Differentiate that and then set y= 1.
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