Update cheatsheet.fr.md

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

@@ -424,18 +424,18 @@ Par ailleurs,$`\phi`$ étant un champ scalaire, sa différentielle exprimée en
 $`\mathbf{d\phi=\left.\dfrac{\partial \phi}{\partial \alpha}\right|_M\cdot dl_{\alpha} + \left.\dfrac{\partial \phi}{\partial \beta}\right|_M\cdot dl_{\beta} + \left.\dfrac{\partial \phi}{\partial \gamma}\right|_M\cdot dl_{\gamma}}`$
 --------------------->
 
-*$`\mathbf{d\phi}`$*$`\;=\dfrac{\partial \phi}{\partial \alpha}\cdot d\alpha + \dfrac{\partial \phi}{\partial \beta}\cdot d\beta + \dfrac{\partial \phi}{\partial \gamma}\cdot d\gamma`$
+*$`\color{blue}{\mathbf{d\phi}}`$*$`\;=\dfrac{\partial \phi}{\partial \alpha}\cdot d\alpha + \dfrac{\partial \phi}{\partial \beta}\cdot d\beta + \dfrac{\partial \phi}{\partial \gamma}\cdot d\gamma`$
 
-*$`\;=
-\dfrac{\partial \phi}{\partial dl_{\alpha}}\,\dfrac{\partial dl_{\alpha}}{\partial \alpha}\, \mathbf{d\alpha}
-+\dfrac{\partial \phi}{\partial dl_{\beta}}\,\dfrac{\partial dl_{\beta}}{\partial \beta}\, \mathbf{d\beta}
-+\dfrac{\partial \phi}{\partial dl_{\gamma}}\,\dfrac{\partial dl_{\gamma}}{\partial \gamma}\, \mathbf{d\gamma}`$*
+*$`\color{blue}{\;=
+\dfrac{\partial \phi}{\partial d\alpha}\,\dfrac{\partial \alpha}{\partial dl_{\alpha}}\, \mathbf{dl_{\alpha}}
++\dfrac{\partial \phi}{\partial d\beta}\,\dfrac{\partial \beta}{\partial dl_{\beta}}\, \mathbf{dl_{\beta}}
++\dfrac{\partial \phi}{\partial d\gamma}\,\dfrac{\partial \gamma}{\partial dl_{\gamma}}\, \mathbf{dl_{\gamma}}}`$*
+
+La comparaison terme à terme de ces deux expressions de $'d\phi`$ donne :
 
-La comparaison terme à terme de ces deux expressions de $d\phi`$ donne l'expression de 
-$`\overrightarrow{grad}\,\phi`$ en coordonnées $`(d\alpha\,,d\beta\,,d\gamma)`$ :
 
 $`\left.\begin{align}{l}
-\d\phi=X_{\alpha}\,dl_{\alpha}+X_{\beta}\,dl_{\beta}+X_{\gamma}\,dl_{\gamma}\\
+X_{\alpha}=dl_{\alpha}+X_{\beta}\,dl_{\beta}+X_{\gamma}\,dl_{\gamma}\\
 \d\phi=\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\\