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\begin{frame}
\frametitle{Implicit Differentiation}

\begin{block}{}
We can use \emph{implicit differentiation}:
\begin{itemize}
\item differentiate both sides of the equation w.r.t. $x$, and
\item then solve for $y'$, that is, for $\frac{dy}{dx}$
\end{itemize}
\end{block}

\begin{exampleblock}{}
We differentiate $x^2 + y^2 = 25$ implicitly.
We have
\begin{talign}
\frac{dy}{dx} = -\frac{x}{y}
\end{talign}
\pause
Find an equation of the tangent at point $(3,4)$.
\pause\medskip

At point $(3,4)$ we have:
\begin{talign}
\frac{dy}{dx} = -\frac{3}{4}
\end{talign}
\pause
Thus the tangent is
\begin{talign}
y - 4 = -\frac{3}{4} (x-3)
\end{talign}
\end{exampleblock}
\vspace{10cm}
\end{frame}