Generate Math Exams and Quizzes in LaTeX and pdf formats

Identifying \(\displaystyle f=9 x^{2} - 9 x - 9\) and \(\displaystyle g=\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right)\) and using the product rule with \(\displaystyle f=9 x^{2} - 9 x - 9 \implies f'=18 x - 9\). This leaves g as \(\displaystyle g = \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right)\) which also requires the product rule. Pushing down in the new product rule \(\displaystyle f=2 x^{2} - x - 3 \implies f'=4 x - 1\) and \(\displaystyle g=- 7 x^{2} - 5 x + 7 \implies g'=- 14 x - 5\). Popping up a level gives \(\displaystyle g'=(- 7 x^{2} - 5 x + 7)(4 x - 1)+(2 x^{2} - x - 3)(- 14 x - 5)\)Popping up again (Back to the original problem) gives \(\displaystyle f'=(9 x^{2} - 9 x - 9)(\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right))+(\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right))(18 x - 9)=\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) \left(9 x^{2} - 9 x - 9\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right) \left(9 x^{2} - 9 x - 9\right) + \left(18 x - 9\right) \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right)\)

Download \(\LaTeX\)

\begin{question}Find the derivative of $y = (9 x^{2} - 9 x - 9)(2 x^{2} - x - 3)(- 7 x^{2} - 5 x + 7)$.
    \soln{9cm}{Identifying $f=9 x^{2} - 9 x - 9$ and $g=\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right)$ and using the product rule with $f=9 x^{2} - 9 x - 9 \implies f'=18 x - 9$. This leaves g as $g = \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right)$ which also requires the product rule. Pushing down in the new product rule $f=2 x^{2} - x - 3 \implies f'=4 x - 1$ and $g=- 7 x^{2} - 5 x + 7 \implies g'=- 14 x - 5$. Popping up a level gives $g'=(- 7 x^{2} - 5 x + 7)(4 x - 1)+(2 x^{2} - x - 3)(- 14 x - 5)$Popping up again (Back to the original problem) gives $f'=(9 x^{2} - 9 x - 9)(\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right))+(\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right))(18 x - 9)=\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) \left(9 x^{2} - 9 x - 9\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right) \left(9 x^{2} - 9 x - 9\right) + \left(18 x - 9\right) \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right)$}

\end{question}

Download Question and Solution Environment\(\LaTeX\)

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}

\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}

\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}

\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue

\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}

HTML for Canvas

<p> <p>Find the derivative of  <img class="equation_image" title=" \displaystyle y = (9 x^{2} - 9 x - 9)(2 x^{2} - x - 3)(- 7 x^{2} - 5 x + 7) " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%20%289%20x%5E%7B2%7D%20-%209%20x%20-%209%29%282%20x%5E%7B2%7D%20-%20x%20-%203%29%28-%207%20x%5E%7B2%7D%20-%205%20x%20%2B%207%29%20" alt="LaTeX:  \displaystyle y = (9 x^{2} - 9 x - 9)(2 x^{2} - x - 3)(- 7 x^{2} - 5 x + 7) " data-equation-content=" \displaystyle y = (9 x^{2} - 9 x - 9)(2 x^{2} - x - 3)(- 7 x^{2} - 5 x + 7) " /> .</p> </p>

HTML for Canvas

<p> <p>Identifying  <img class="equation_image" title=" \displaystyle f=9 x^{2} - 9 x - 9 " src="/equation_images/%20%5Cdisplaystyle%20f%3D9%20x%5E%7B2%7D%20-%209%20x%20-%209%20" alt="LaTeX:  \displaystyle f=9 x^{2} - 9 x - 9 " data-equation-content=" \displaystyle f=9 x^{2} - 9 x - 9 " />  and  <img class="equation_image" title=" \displaystyle g=\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right) " src="/equation_images/%20%5Cdisplaystyle%20g%3D%5Cleft%28-%207%20x%5E%7B2%7D%20-%205%20x%20%2B%207%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20-%20x%20-%203%5Cright%29%20" alt="LaTeX:  \displaystyle g=\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right) " data-equation-content=" \displaystyle g=\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right) " />  and using the product rule with  <img class="equation_image" title=" \displaystyle f=9 x^{2} - 9 x - 9 \implies f'=18 x - 9 " src="/equation_images/%20%5Cdisplaystyle%20f%3D9%20x%5E%7B2%7D%20-%209%20x%20-%209%20%5Cimplies%20f%27%3D18%20x%20-%209%20" alt="LaTeX:  \displaystyle f=9 x^{2} - 9 x - 9 \implies f'=18 x - 9 " data-equation-content=" \displaystyle f=9 x^{2} - 9 x - 9 \implies f'=18 x - 9 " /> . This leaves g as  <img class="equation_image" title=" \displaystyle g = \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right) " src="/equation_images/%20%5Cdisplaystyle%20g%20%3D%20%5Cleft%28-%207%20x%5E%7B2%7D%20-%205%20x%20%2B%207%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20-%20x%20-%203%5Cright%29%20" alt="LaTeX:  \displaystyle g = \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right) " data-equation-content=" \displaystyle g = \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right) " />  which also requires the product rule. Pushing down in the new product rule  <img class="equation_image" title=" \displaystyle f=2 x^{2} - x - 3 \implies f'=4 x - 1 " src="/equation_images/%20%5Cdisplaystyle%20f%3D2%20x%5E%7B2%7D%20-%20x%20-%203%20%5Cimplies%20f%27%3D4%20x%20-%201%20" alt="LaTeX:  \displaystyle f=2 x^{2} - x - 3 \implies f'=4 x - 1 " data-equation-content=" \displaystyle f=2 x^{2} - x - 3 \implies f'=4 x - 1 " />  and  <img class="equation_image" title=" \displaystyle g=- 7 x^{2} - 5 x + 7 \implies g'=- 14 x - 5 " src="/equation_images/%20%5Cdisplaystyle%20g%3D-%207%20x%5E%7B2%7D%20-%205%20x%20%2B%207%20%5Cimplies%20g%27%3D-%2014%20x%20-%205%20" alt="LaTeX:  \displaystyle g=- 7 x^{2} - 5 x + 7 \implies g'=- 14 x - 5 " data-equation-content=" \displaystyle g=- 7 x^{2} - 5 x + 7 \implies g'=- 14 x - 5 " /> . Popping up a level gives  <img class="equation_image" title=" \displaystyle g'=(- 7 x^{2} - 5 x + 7)(4 x - 1)+(2 x^{2} - x - 3)(- 14 x - 5) " src="/equation_images/%20%5Cdisplaystyle%20g%27%3D%28-%207%20x%5E%7B2%7D%20-%205%20x%20%2B%207%29%284%20x%20-%201%29%2B%282%20x%5E%7B2%7D%20-%20x%20-%203%29%28-%2014%20x%20-%205%29%20" alt="LaTeX:  \displaystyle g'=(- 7 x^{2} - 5 x + 7)(4 x - 1)+(2 x^{2} - x - 3)(- 14 x - 5) " data-equation-content=" \displaystyle g'=(- 7 x^{2} - 5 x + 7)(4 x - 1)+(2 x^{2} - x - 3)(- 14 x - 5) " /> Popping up again (Back to the original problem) gives  <img class="equation_image" title=" \displaystyle f'=(9 x^{2} - 9 x - 9)(\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right))+(\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right))(18 x - 9)=\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) \left(9 x^{2} - 9 x - 9\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right) \left(9 x^{2} - 9 x - 9\right) + \left(18 x - 9\right) \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right) " src="/equation_images/%20%5Cdisplaystyle%20f%27%3D%289%20x%5E%7B2%7D%20-%209%20x%20-%209%29%28%5Cleft%28-%2014%20x%20-%205%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20-%20x%20-%203%5Cright%29%20%2B%20%5Cleft%284%20x%20-%201%5Cright%29%20%5Cleft%28-%207%20x%5E%7B2%7D%20-%205%20x%20%2B%207%5Cright%29%29%2B%28%5Cleft%28-%207%20x%5E%7B2%7D%20-%205%20x%20%2B%207%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20-%20x%20-%203%5Cright%29%29%2818%20x%20-%209%29%3D%5Cleft%28-%2014%20x%20-%205%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20-%20x%20-%203%5Cright%29%20%5Cleft%289%20x%5E%7B2%7D%20-%209%20x%20-%209%5Cright%29%20%2B%20%5Cleft%284%20x%20-%201%5Cright%29%20%5Cleft%28-%207%20x%5E%7B2%7D%20-%205%20x%20%2B%207%5Cright%29%20%5Cleft%289%20x%5E%7B2%7D%20-%209%20x%20-%209%5Cright%29%20%2B%20%5Cleft%2818%20x%20-%209%5Cright%29%20%5Cleft%28-%207%20x%5E%7B2%7D%20-%205%20x%20%2B%207%5Cright%29%20%5Cleft%282%20x%5E%7B2%7D%20-%20x%20-%203%5Cright%29%20" alt="LaTeX:  \displaystyle f'=(9 x^{2} - 9 x - 9)(\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right))+(\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right))(18 x - 9)=\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) \left(9 x^{2} - 9 x - 9\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right) \left(9 x^{2} - 9 x - 9\right) + \left(18 x - 9\right) \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right) " data-equation-content=" \displaystyle f'=(9 x^{2} - 9 x - 9)(\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right))+(\left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right))(18 x - 9)=\left(- 14 x - 5\right) \left(2 x^{2} - x - 3\right) \left(9 x^{2} - 9 x - 9\right) + \left(4 x - 1\right) \left(- 7 x^{2} - 5 x + 7\right) \left(9 x^{2} - 9 x - 9\right) + \left(18 x - 9\right) \left(- 7 x^{2} - 5 x + 7\right) \left(2 x^{2} - x - 3\right) " /> </p> </p>