Derivative-practice-chain-rule-Leibniz-notation.tex

\Section{Derivative practice---chain rule, Leibniz notation}


\begin{multicols}{2}
 Given
 \begin{equation*}
  \begin{split}
    \OuterStyle{y} &= \OuterStyle{2 u^2 + 4 u}
    \\
    \InnerStyle{u} &= \InnerStyle{-2 x^2 + 6x - 5}
  \end{split}
 \end{equation*}
 answer the following.
 \bigskip

 \begin{ProblemSet}[pencil space=1.25in]

  \begin{Problem}
   What is $\displaystyle{\Where{\OuterStyle{y}}{\InnerStyle{u=3}}}$?
  \end{Problem}

  \begin{Problem}
   What is $\displaystyle{\Where{\InnerStyle{u}}{x=2}}$?
  \end{Problem}

  \begin{Problem}
   What is $\displaystyle\Where{y}{x=2}?$
  \end{Problem}

  \begin{Problem}
   What is $\displaystyle{\InnerStyle{\Deriv{u}{x}}}$?
  \end{Problem}

  \begin{Problem}
   What is $\displaystyle{\Where{\InnerStyle{\Deriv{u}{x}}}{x=2}}$?
  \end{Problem}

  \begin{Problem}
   What is $\displaystyle{\OuterStyle{\Deriv{y}{u}}}$?
  \end{Problem}

  \begin{Problem}
   What is $\displaystyle{\Where{\OuterStyle{\Deriv{y}{u}}}{\InnerStyle{u=3}}}$?
  \end{Problem}

  \begin{Problem}
   What is $\displaystyle\Deriv{y}{x}$?
  \end{Problem}

  \begin{Problem}
   What is $\displaystyle\Where{\Deriv{y}{x}}{x=2}$?
  \end{Problem}

 \end{ProblemSet}
\end{multicols}

Given
\begin{equation*}
 \begin{split}
   y &= -u^3 + 2 u^2
   \\
   u &= x^2 - 3x - 2
 \end{split}
\end{equation*}
answer the following.
\bigskip

\begin{ProblemSet}[pencil space=2in]

 \begin{Problem}[pencil space=1in]
  What is $\displaystyle{\Where{y}{x=-2}}$?
 \end{Problem}

 \begin{Problem}
  What is $\displaystyle{\Deriv{y}{x}}$?
 \end{Problem}

 \begin{Problem}
  What is $\displaystyle{\Where{\Deriv{y}{x}}{x=-2}}$?
 \end{Problem}

\end{ProblemSet}

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