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Math Help - Implicit Differentiation

  1. #1
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    Implicit Differentiation

    Use Implicit Differentiation:

    (x^3) + (y^3) = 6xy

    So I got:

    (3x^2) + (3y^2)(dy/dx) = (0)(x*dy/dx) + (y)(1)

    But the answer I got was wrong...any help?
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  2. #2
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    Quote Originally Posted by Dickson View Post
    Use Implicit Differentiation:

    (x^3) + (y^3) = 6xy

    So I got:

    (3x^2) + (3y^2)(dy/dx) = (0)(x*dy/dx) + (y)(1)
    Why "(0)(x*dy/dx)? Surely you aren't thinking "the derivative of 6 is 0" because you are differentiating y here, not 6. That first term should be 6x*dy/dx. And, for course, the second is 6y, not just y.

    But the answer I got was wrong...any help?
    In general, if c is a constant, (cf(x))'= cf'(x). If you really WANT to use the product rule, (cf(x))'= 0f(x)+ cf'(x)= cf'(x).

    You might write, above, (6xy)'= (0)xy+ (6y)+ (6x)y'= 6xdy/dx+ 6y.
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  3. #3
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    I surely was thinking 6 was 0...god. Anyway thanks for the help.
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  4. #4
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    Well, 6 is close to 0!
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