Specify noDerivative and zeroDerivative.

Closes #2840
(And using those formulas, but reworked based on the examples.)

chapters/functions.tex

@@ -1414,6 +1414,12 @@ \subsection{Using the Derivative Annotation}\label{using-the-derivative-annotati
   //annotation(derivative(order=2) = f_general_der2);
 end f_general_der;
 \end{lstlisting}
+In the example above \lstinline!zeroDerivative=y! imply that
+\begin{eqnarray*}
+\frac{d}{dt}f(x(t),y(t))&=&\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{dy}{dt}\\
+&=&\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\cdot 0\\
+&=&\frac{\partial f}{\partial x}\frac{dx}{dt}
+\end{eqnarray*}
 \end{nonnormative}
 
 \begin{itemize}
@@ -1459,6 +1465,13 @@ \subsection{Using the Derivative Annotation}\label{using-the-derivative-annotati
 \end{lstlisting}
 This is useful if \lstinline!g! represents the major computational
 effort of \lstinline!fg!.
+
+Therefore \lstinline!f_der! indirectly includes the derivative with respect to \lstinline!y! as follows:
+\begin{eqnarray*}
+\frac{d}{dt}fg(x(t))&=&\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{\partial g}{\partial x}\frac{dx}{dt}\\
+&=&(\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y}\frac{\partial g}{\partial x})\frac{dx}{dt}\\
+&=&\textrm{f\_der}(x,y)\frac{dx}{dt}
+\end{eqnarray*}
 \end{nonnormative}
 
 \subsection{Partial Derivatives of Functions}\label{partial-derivatives-of-functions}