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Math Help - Tricky Implicit Differentiation

  1. March 12th 2012, 08:39 AM #1
    charlottewill
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    Unhappy Tricky Implicit Differentiation

    Hi,

    How could I possibly differentiate x = a - 1/(kt-c) where c is an integration factor in order to provide the equation

    dx/dt = k(a-x)(b-x)

    assuming that a = b
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  2. March 12th 2012, 02:38 PM #2
    Ridley
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    Re: Tricky Implicit Differentiation

    \frac{dx}{dt}=\frac{k}{(kt-c)^2}=k\left(\frac{1}{kt-c}\right)\left(\frac{1}{kt-c}\right)=k\left(a - a - \frac{-1}{kt-c}\right)\left(a - a - \frac{-1}{kt-c}\right)=k(a-x)(a-x)
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