<div class="dem1">
 Avec \( r=sqrt(x^2+y^2+z^2) ) , on tire de \(r^2=x^2+y^2+z^2) que   \(  r \frac{\partial r}{\partial x}= x ), 
 \(  r \frac{\partial r}{\partial y}= y ), \(  r \frac{\partial r}{\partial z}= z ).
 Donc, 
 <p> <center>\(  F(M)=(\frac{x}{r^3},\frac{y}{r^3},\frac{z}{r^3}) )</center></p>
 et
 <p> <center>\(  div(F)(M)= (\frac{1}{r^3}-\frac{3x}{r^4}\frac{\partial r}{\partial x})-
  (\frac{1}{r^3}-\frac{3y}{r^4}\frac{\partial r}{\partial y})-
  (\frac{1}{r^3}-\frac{3z}{r^4}\frac{\partial r}{\partial z}) )</center></p>
  
  <p> <center>=\(\frac{3}{r^3} -\frac{3x^2}{r^5}-\frac{3y^2}{r^5}-\frac{3z^2}{r^5} =0 )</center></p>
</div>