Update cheatsheet.fr.md

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

@@ -443,9 +443,17 @@ référentirl d'inertie, force centrale
 
 figure à faire.
 
-$`\overrightarrow{F}\cdot\overrightarrow{dl}=m\,\overrightarrow{\mathscr{v}}\times\overrightarrow{\mathscr{v}}\,dt`$
+$`\begin{align}
+\overrightarrow{F}\cdot\overrightarrow{dl}&=\left(m\,\dfrac{d\overrightarrow{\mathscr{v}}}{dt}\right)\cdot\big(\overrightarrow{\mathscr{v}}\,dt\big)\\
+&=m\,\left(\dfrac{d\overrightarrow{\mathscr{v}}}{dt}\cdot\overrightarrow{\mathscr{v}}\right)\,dt\\
+&=m\,\left(\dfrac{1}{2}\,\dfrac{d\big(\overrightarrow{\mathscr{v}}\cdot\overrightarrow{\mathscr{v}}\big)}{dt}\,dt\\
+&=m\,\left(\dfrac{1}{2}\,\dfrac{d\,\mathscr{v}^2}{dt}\,dt\\
+&=d\left(\dfrac{m\,\mathscr{v}^2}{2}\right)\\
+\end{array}`$
+
+$`\overrightarrow{F}\cdot\overrightarrow{dl}=\left(m\,\dfrac{d\overrightarrow{\mathscr{v}}}{dt}\right)\cdot\big(\overrightarrow{\mathscr{v}}\,dt\big)`$
+
 
-$`\overrightarrow{F}\cdot\overrightarrow{dl}=\underset{\overrightarrow{F}=m\overrightarrow{a}}{m\,\overrightarrow{\mathscr{a}}\times\overrightarrow{\mathscr{v}}\,dt`$
 
 ![](from-potential-to-potential-energy_v2_L800.gif)