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Math Help - implicit differentiation

  1. #1
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    implicit differentiation

    I have a question about implicit differentiation.


    In the case of differentiating the expression x^3+y^3=6xy the right hand side becomes 6xy'+6y where y is regarded as a function of x.


    using the product rule f'g+g'f


     f = 6x


    g = y

    then



    (6x)' y + 6y'


    so I get 6y+6y'


    which is wrong.


    Why is the right hand side equal to 6xy'+6y?


    I (think) I know the key is that y is a function of x but somehow its not clicking as to why the answer is as it is.
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    Re: implicit differentiation

    Quote Originally Posted by kingsolomonsgrave View Post
    I have a question about implicit differentiation.


    In the case of differentiating the expression x^3+y^3=6xy the right hand side becomes 6xy'+6y where y is regarded as a function of x.


    using the product rule f'g+g'f


     f = 6x


    g = y

    then



    (6x)' y + 6y'


    so I get 6y+6y'


    which is wrong.


    Why is the right hand side equal to 6xy'+6y?


    I (think) I know the key is that y is a function of x but somehow its not clicking as to why the answer is as it is.
    You differentated f is both parts of your product rule

    It should be

    f(x)=6x \implies f'(x)=6 \quad g(x)=y \implies g'(x)=y'

    So

    \frac{d}{dx}(fg)=f'g+fg'=6y+(6x)y'
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  3. #3
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    Re: implicit differentiation

    thank you! I wrote my prof and he just wrote back - it should be 6y+6xy'

    I was like....yes, we know this, it's in the text book....talk about not helpful.

    This forum (and the helpful math experts that populate it) save my life.

    thanks again
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