Update cheatsheet.fr.md

12.temporary_ins/08.grad-div-rot/70.combinaisons-of-operators/20.overview/cheatsheet.fr.md

@@ -80,4 +80,23 @@ $`\quad =
 
 $`\color{blue}{div\,\overrightarrow{U}=\dfrac{\partial U_x}{\partial x}+\dfrac{\partial U_y}{\partial y}+\dfrac{\partial U_z}{\partial z}}`$
 
+      La divergence d'un champ vectoriel est un champ scalaire.   
+      Le gradient d'un champ scalaire $`f`$ est le champ vectoriel,
+      qui s'exprime en coordonnées cartésiennes :
+
+$`\overrightarrow{grad}\,f=\left(
+\begin{array}{l}
+\dfrac{\partial f}{\partial x}\\
+\dfrac{\partial f}{\partial y}\\
+\dfrac{\partial f}{\partial z}
+\end{array}\right)`$
+
+      donc :
 
+$`\overrightarrow{grad}\big(div\,\overrightarray{U}\big)`$
+$`\quad = 
+\begin{array}{l}
+\dfrac{\partial}{\partial x}\left( \color{blue}{\dfrac{\partial U_x}{\partial x}} \right)\\
+\dfrac{\partial}{\partial y}\left( \color{blue}{\dfrac{\partial U_y}{\partial y}} \right)\\
+\dfrac{\partial}{\partial z}\left( \color{blue}{\dfrac{\partial U_z}{\partial z}} \right)
+\end{array}\right)`$
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