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Math Help - differentiating this equation

  1. #1
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    Red face differentiating this equation

    HI I have attached a picture of the equation which I have problem with.

    I need to differentiate T with respect to T0, so dT/dT0

    D, L, lambda and C are constants.

    I would apperciate if anyone can help me differentiating the above equation

    (link to the image Yfrog Image : yfrog.com/mvequationj)


    differentiating this equation-equation.jpg
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  2. #2
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    We differentiate the LHS with the chain rule:

    <br />
\frac{d}{dT_0}T^2 = 2 T \frac{dT}{dT_0}

    We differentiate the RHS with the usual power rule:

    \displaystyle \frac{d}{dT_0}( T_0^2+f T_0^{-2} ) =  2 T_0 - 2 f T_0^{-3}

    f is just the combined constants. Equating both sides and canceling the 2, we get

     \displaystyle T \frac{dT}{dT_0} =  T_0 -  f T_0^{-3}

    We still have a free T, so we need to replace it with an expression derived from the first equation.

    \displaystyle \frac{dT}{dT_0} = T^{-1} (T_0 -  f T_0^{-3}) = ( T_0^2+f T_0^{-2})^{-1/2}(T_0 -  f T_0^{-3})

    And I think you are done.
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  3. #3
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    Thans
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