Added higher derivs

chapters/sections/partial_total_diff.tex

@@ -292,7 +292,7 @@ They denote the connecting line between $x$ and $y$.
 \end{center}
 
 \begin{thm}[Intermediate value theorem for $\realn$-valued functions]
-    Let $U \subset \realn^n$ be oppen, $x, y \in U$ and $\cline \subset U$.
+    Let $U \subset \realn^n$ be open, $x, y \in U$ and $\cline \subset U$.
     Now let $f: U \rightarrow \realn$ differentiable on $\oline$ and continuous in $x, y$. Then 
     \[
         \exists \xi \in \cline: ~~f(y) - f(x) = Df(\xi) (y-x)