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anonymous
 one year ago
Please, help me
anonymous
 one year ago
Please, help me

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Proof \[\frac{ \textbf{x } \textbf{x}_i }{ \left \textbf{x}  {\textbf{x}_i} \right^3 } = \bigtriangledown \left( \frac{ 1 }{ xx' } \right)\]

TheCatMan
 one year ago
Best ResponseYou've already chosen the best response.0i say to find the area of the triangle using other info to the question (if there is none i have no clue) distribute to the right side of the equation and cross eliminate to solve

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1WHAT THE! SOlving has nothing to do with writing a complete proof. And I don't know which subject this came from. It could be from some grad school Math course :S

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1I know that for proofs like this you either start at the left apply some theorems...definitions lalalalalla and achieve the right or start at the right apply some theorems...definitions lalalla and achieve the left.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0mathematical physics

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1that could be in the later part of Mathematical Physics...... I only know the first half and have not done a proof like this

TheCatMan
 one year ago
Best ResponseYou've already chosen the best response.0i wish i could help but im dumber than a fart in a crowded room.

alekos
 one year ago
Best ResponseYou've already chosen the best response.0it really means nothing without some sort of context. tel us more about the problem

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3here are some steps: we can write: \[{\mathbf{x}}  {{\mathbf{x}}_i} = {\mathbf{r}}\] where: \[{\mathbf{r}} \cdot {\mathbf{r}} = {x^2} + {y^2} + {z^2}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3so we have: \[\large \begin{gathered} \frac{\partial }{{\partial x}}\left( {\frac{1}{r}} \right) = \frac{\partial }{{\partial x}}\left( {\frac{1}{{\sqrt {{x^2} + {y^2} + {z^2}} }}} \right) =  \frac{x}{{{{\left( {\sqrt {{x^2} + {y^2} + {z^2}} } \right)}^3}}} \hfill \\ \hfill \\ \frac{\partial }{{\partial y}}\left( {\frac{1}{r}} \right) = \frac{\partial }{{\partial y}}\left( {\frac{1}{{\sqrt {{x^2} + {y^2} + {z^2}} }}} \right) =  \frac{y}{{{{\left( {\sqrt {{x^2} + {y^2} + {z^2}} } \right)}^3}}} \hfill \\ \hfill \\ \frac{\partial }{{\partial z}}\left( {\frac{1}{r}} \right) = \frac{\partial }{{\partial z}}\left( {\frac{1}{{\sqrt {{x^2} + {y^2} + {z^2}} }}} \right) =  \frac{z}{{{{\left( {\sqrt {{x^2} + {y^2} + {z^2}} } \right)}^3}}} \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3\[\begin{gathered} \frac{\partial }{{\partial x}}\left( {\frac{1}{r}} \right) = \frac{\partial }{{\partial x}}\left( {\frac{1}{{\sqrt {{x^2} + {y^2} + {z^2}} }}} \right) =  \frac{x}{{{{\left( {\sqrt {{x^2} + {y^2} + {z^2}} } \right)}^3}}} \hfill \\ \hfill \\ \frac{\partial }{{\partial y}}\left( {\frac{1}{r}} \right) = \frac{\partial }{{\partial y}}\left( {\frac{1}{{\sqrt {{x^2} + {y^2} + {z^2}} }}} \right) =  \frac{y}{{{{\left( {\sqrt {{x^2} + {y^2} + {z^2}} } \right)}^3}}} \hfill \\ \hfill \\ \frac{\partial }{{\partial z}}\left( {\frac{1}{r}} \right) = \frac{\partial }{{\partial z}}\left( {\frac{1}{{\sqrt {{x^2} + {y^2} + {z^2}} }}} \right) =  \frac{z}{{{{\left( {\sqrt {{x^2} + {y^2} + {z^2}} } \right)}^3}}} \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3and finally: \[\Large \nabla \left( {\frac{1}{r}} \right) =  \frac{{\mathbf{r}}}{{{r^3}}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0awesome @Michele_Laino , thank you

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i also thank to @TheCatMan , @UsukiDoll , @alekos

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1what @Michele_Laino latexed is similar to an example from a book I had to use almost a year ago. There was partial derivatives, product rule, and chain rule involved.
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