40/177
\begin{frame}
  \frametitle{2nd Midterm Exam - Review}

  \begin{exampleblock}{}
    Find the derivative of
    \begin{align*}
      f(x) = x\cdot e^{\frac{1}{x}}
    \end{align*}
    \pause
    We have:
    \begin{align*}
      f'(x) 
      &= \mpause[1]{ x\cdot \frac{d}{dx} e^{\frac{1}{x}} + e^{\frac{1}{x}} \cdot \frac{d}{dx} x } \\
      &\mpause[2]{= x\cdot e^{\frac{1}{x}}\cdot \frac{d}{dx} \frac{1}{x} + e^{\frac{1}{x}} } \\
      &\mpause[3]{= x\cdot e^{\frac{1}{x}}\cdot (-1)x^{-2} + e^{\frac{1}{x}} } \\
      &\mpause[4]{= e^{\frac{1}{x}}(1  -\frac{1}{ x } ) } 
    \end{align*}
  \end{exampleblock}
\end{frame}