Thread: Partial & Implicit Problem ! Help !

1. Partial & Implicit Problem ! Help !

2. For the first

$\displaystyle \frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}} = \frac{{{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}}} {{{R_1}{R_2}{R_3}}} \Leftrightarrow R = \frac{{{R_1}{R_2}{R_3}}} {{{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}}}.$

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

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

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

3. $\displaystyle \frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}}$

Differentiate both side with respect to $\displaystyle R_1$

$\displaystyle \frac{-1}{(R)^2} \frac{\partial R}{\partial R_1}= \frac{-1}{(R_1)^2}$

4. 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 $\displaystyle \partial u/\partial x$ is it ?