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Math Help - Partial & Implicit Problem ! Help !

  1. #1
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    Partial & Implicit Problem ! Help !

    Last edited by Zachary; August 5th 2009 at 10:30 PM.
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  2. #2
    Senior Member DeMath's Avatar
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    For the first

    \frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}} = \frac{{{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}}}<br />
{{{R_1}{R_2}{R_3}}} \Leftrightarrow R = \frac{{{R_1}{R_2}{R_3}}}<br />
{{{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}}}.

    \frac{{\partial R}}{{\partial {R_1}}} = \frac{{{{\left( {{R_1}{R_2}{R_3}} \right)}^\prime }_{{R_1}}\left( {{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}} \right) - {R_1}{R_2}{R_3}{{\left( {{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}} \right)}^\prime }_{{R_1}}}}{{{{\left( {{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}} \right)}^2}}} =

    = \frac{{{R_2}{R_3}\left( {{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}} \right) - {R_1}{R_2}{R_3}\left( {{R_2} + {R_3}} \right)}}{{{{\left( {{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}} \right)}^2}}} =

    = \frac{{{R_2}{R_3}}}{{{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}}} - \frac{{{R_1}{R_2}{R_3}\left( {{R_2} + {R_3}} \right)}}{{{{\left( {{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}} \right)}^2}}}.
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  3. #3
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    \frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}}

    Differentiate both side with respect to R_1

    \frac{-1}{(R)^2} \frac{\partial R}{\partial R_1}= \frac{-1}{(R_1)^2}
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  4. #4
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    The 1st problem i use quotient rule , no wonder cannot solved.

    Thank you Demath & songoku (DRAGON BALL).


    Who else know the second problem ?

    How can solve it without given the u equation ? cannot calculate \partial u/\partial x is it ?
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