Update cheatsheet.fr.md

12.temporary_ins/08.conservative-vector-fields/20.conservative-vector-fields-properties/20.overview/cheatsheet.fr.md

@@ -418,7 +418,7 @@ $`\begin{align}
 
 $`\color{brown}{\mathbf{\; = X_{\alpha}\,dl_{\alpha}+X_{\beta}\,dl_{\beta}+X_{\gamma}\,dl_{\gamma}}}`$
 
-Par ailleurs,$`\phi`$ étant un champ scalaire, sa différentielle exprimée en fonction des $`(d\alpha\,,d\beta\,,d\gamma)`$ s'écrit :
+Par ailleurs,$`\phi`$ étant un champ scalaire, sa différentielle exprimée en fonction des $`d\alpha\,,d\beta\,,d\gamma`$ s'écrit :
 
 <!---------------------
 $`\mathbf{d\phi=\left.\dfrac{\partial \phi}{\partial \alpha}\right|_M\cdot dl_{\alpha} + \left.\dfrac{\partial \phi}{\partial \beta}\right|_M\cdot dl_{\beta} + \left.\dfrac{\partial \phi}{\partial \gamma}\right|_M\cdot dl_{\gamma}}`$
@@ -426,14 +426,14 @@ $`\mathbf{d\phi=\left.\dfrac{\partial \phi}{\partial \alpha}\right|_M\cdot dl_{\
 
 *$`\mathbf{d\phi}`$*$`\;=\dfrac{\partial \phi}{\partial \alpha}\cdot d\alpha + \dfrac{\partial \phi}{\partial \beta}\cdot d\beta + \dfrac{\partial \phi}{\partial \gamma}\cdot d\gamma`$
 
-$`\mathbf{\;=
-\dfrac{\partial \phi}{\partial dl_{\alpha}}\,\dfrac{\partial dl_{\alpha}}{\partial \alpha}\, d\alpha
-+\dfrac{\partial \phi}{\partial dl_{\beta}}\,\dfrac{\partial dl_{\beta}}{\partial \beta}\, d\beta
-+\dfrac{\partial \phi}{\partial dl_{\gamma}}\,\dfrac{\partial dl_{\gamma}}{\partial \gamma}\, d\gamma}`$
+*$`\;=
+\dfrac{\partial \phi}{\partial dl_{\alpha}}\,\dfrac{\partial dl_{\alpha}}{\partial \alpha}\, \mathbf{d\alpha}
++\dfrac{\partial \phi}{\partial dl_{\beta}}\,\dfrac{\partial dl_{\beta}}{\partial \beta}\, \mathbf{d\beta}
++\dfrac{\partial \phi}{\partial dl_{\gamma}}\,\dfrac{\partial dl_{\gamma}}{\partial \gamma}\, \mathbf{d\gamma}`$*
+
+La comparaison terme à terme de ces deux expressions de $d\phi`$ donne l'expression de 
+$`\overrightarrow{grad}\,\phi`$ en coordonnées $`(d\alpha\,,d\beta\,,d\gamma)`$ :
 
-$`\;=\,\dfrac{\partial \phi}{\partial dl_{\alpha}}\,\dfrac{\partial dl_{\alpha}}{\partial \alpha}\, d\alpha`$
-$`+\dfrac{\partial \phi}{\partial dl_{\beta}}\,\dfrac{\partial dl_{\beta}}{\partial \beta}\, d\beta}
-+\dfrac{\partial \phi}{\partial dl_{\gamma}}\,\dfrac{\partial dl_{\gamma}}{\partial \gamma}\, d\gamma}`$