\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}