diff --git a/doc/rcfs.pdf b/doc/rcfs.pdf
index 803d7f85f609cfaa0b7721b47fac5022daa30f10..f4f80d69003379d7d30abc81bf4db4dfb3f63ffd 100644
Binary files a/doc/rcfs.pdf and b/doc/rcfs.pdf differ
diff --git a/doc/rcfs.tex b/doc/rcfs.tex
index 3a03dc88cbba575094520bd41178b6d0daade9c0..626f12e15d45fc1f91b4cab56d2e88dc81b78842 100644
--- a/doc/rcfs.tex
+++ b/doc/rcfs.tex
@@ -2848,10 +2848,10 @@ By leveraging this matrix formulation, the curvature in \eqref{eq:curvature0} ca
 \end{equation}
 with selection matrices $\bm{S}_A=\bm{s}_{1,1} \bm{s}_{2,2}^\trsp - \bm{s}_{1,2} \bm{s}_{2,1}^\trsp$ and $\bm{S}_B=\bm{s}_{1,1} \bm{s}_{1,1}^\trsp + \bm{s}_{1,2} \bm{s}_{1,2}^\trsp$.
 
-With this formulation, by using the derivative property $(fg)'=f'g+fg'$, the derivatives of \eqref{eq:curvature0} w.r.t $\bm{x}$ form the Jacobian
+With this formulation, by using the derivative property $(fg)'=f'g+fg'$, and by observing that $\bm{S}_B$ is a symmetric matrix and that $\bm{S}_A$ is an asymmetric matrix, the derivatives of \eqref{eq:curvature0} w.r.t $\bm{x}$ form the Jacobian
 \begin{equation}
 	\bm{J}(\bm{x}) = \frac{\partial \kappa(\bm{x})}{\partial\bm{x}} = 
-	2 \; (\bm{x}^\trsp \bm{S}_B \bm{x})^{-\frac{3}{2}} \; \bm{S}_A \bm{x}  -
+	(\bm{x}^\trsp \bm{S}_B \bm{x})^{-\frac{3}{2}} \; (\bm{S}_A+\bm{S}_A^\trsp) \bm{x}  -
 	3 \; (\bm{x}^\trsp \bm{S}_A \bm{x}) \; (\bm{x}^\trsp \bm{S}_B \bm{x})^{-\frac{5}{2}} \; \bm{S}_B \bm{x}. 
 	\label{eq:diff_curvature}
 \end{equation}