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\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle

\subsection{The definition of the derivative}

\begin{example}
Find \( f'(x) \) for the function \( f(x)=\sqrt{x} \). 
\end{example}

\subsubsection*{Solution }

Using just the definition of the derivative, then plugging in for the function
\[
f(x)=\sqrt{x},\]
we have 

\begin{eqnarray*}
f'(x) & = & \lim _{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}\\
 & = & \lim _{h\rightarrow 0}\frac{\sqrt{x+h}-\sqrt{x}}{h}.
\end{eqnarray*}



\subsubsection*{Next step}
\end{document}
