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Update chapters/functions.tex
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Co-authored-by: Elena Shmoylova <eshmoylova@users.noreply.github.com>
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HansOlsson and eshmoylova committed Feb 22, 2021
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Expand Up @@ -1416,7 +1416,7 @@ \subsection{Using the Derivative Annotation}\label{using-the-derivative-annotati
\end{lstlisting}
In the example above \lstinline!zeroDerivative=y! implies 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 o}\frac{do}{dt}\\
\frac{d}{dt}f(x(t),y(t),o(t))&=&\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{dy}{dt}+\frac{\partial f}{\partial o}\frac{do}{dt}\\
&=&\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\cdot 0+\frac{\partial f}{\partial o}\cdot 0\\
&=&\frac{\partial f}{\partial x}\frac{dx}{dt}
\end{eqnarray*}
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