Update cheatsheet.fr.md

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

@@ -469,13 +469,23 @@ dl_z=dz \Longrightarrow \dfrac{\partial z}{\partial l_z}=1\\
 $`\Longrightarrow\color{brown}{\mathbf{
 \overrightarrow{grad}\,\phi=
 \dfrac{\partial \phi}{\partial \rho}\,\overrightarrow{e_{\rho}}
-+\dfrac{1}{\rho}\,\dfrac{\partial \phi}{\partial y}\,\overrightarrow{e_{\varphi}}
++\dfrac{1}{\rho}\,\dfrac{\partial \phi}{\partial \varphi}\,\overrightarrow{e_{\varphi}}
 +\dfrac{\partial \phi}{\partial z}\,\overrightarrow{e_z}
 }}`$
 
 ##### Expression du gradient en coordonnées sphériques
 
-
+$`\left.\begin{align}
+dl_r=dr\Longrightarrow \dfrac{\partial r}{\partial l_r}=1\\
+dl_{\theta}=r\,d{\theta} \Longrightarrow \dfrac{\partial r}{\partial l_r}=\dfrac{1}{r}\\
+dl_{\varphi}=r\,\sin\theta\,d\varphi \Longrightarrow \dfrac{\partial l_{\varphi}}{\partial l_{\varphi}}=\dfrac{1}{r\,\sin\theta}\\
+\end{align}\right\}`$
+$`\Longrightarrow\color{brown}{\mathbf{
+\overrightarrow{grad}\,\phi=
+\dfrac{\partial \phi}{\partial r}\,\overrightarrow{e_r}
++\dfrac{1}{r}\,\dfrac{\partial \phi}{\partial \theta}\,\overrightarrow{e_{\theta}}
++\dfrac{1}{r\,\sin\theta}\,\dfrac{\partial \phi}{\partial \varphi}\,\overrightarrow{e_{\varphi}}
+}}`$