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\begin{frame}
  \frametitle{Fundamental Theorem of Calculus}
  
  \fundamental
  \medskip
  
  \begin{exampleblock}{}
    Find \vspace{-1ex}
    \begin{talign}
      g(x) = \frac{d}{dx} \int_1^{x^4} \sec t\; dt
    \end{talign}
    \pause
    
    Lets introduce a name for the integral without $x^4$:
    \begin{talign}
      f(x) = \int_1^{x} \sec t \,dt &&\mpause[1]{f'(x) =}\mpause{ \sec x}
    \end{talign}
    \pause\pause\pause
    Then
    \begin{talign}
      g(x) = \mpause[1]{ \frac{d}{dx} f(x^4) }
      \mpause{ = f'(x^4)\cdot 4x^3 }
      \mpause{ = \sec(x^4)\cdot 4x^3 }
    \end{talign}
  \end{exampleblock} 
  \vspace{10cm} 
\end{frame}