\begin{frame} \frametitle{Differentiation Rules: Chain Rule} \begin{block}{} \begin{malign} (f\circ g)'(x) \;=\; f'(g(x)) \cdot g'(x) \end{malign} \end{block} \begin{exampleblock}{} Differentiate \begin{talign} f(x) = (2x+1)^5 \cdot (x^3-x+1)^4 \end{talign} \pause We have \begin{talign} f'(x) &= \mpause[1]{ (2x+1)^5 \cdot \frac{d}{dx} [(x^3-x+1)^4] }\\ &\mpause[1]{ \hspace{1cm} + (x^3-x+1)^4 \cdot \frac{d}{dx} [(2x+1)^5] }\\ &\mpause[2]{= (2x+1)^5 \cdot 4(x^3-x+1)^3\cdot (3x^2-1) }\\ &\mpause[2]{\hspace{1cm} + (x^3-x+1)^4 \cdot 5(2x+1)^4\cdot 2 } \end{talign} \end{exampleblock} \vspace{10cm} \end{frame}