Generate Math Exams and Quizzes in LaTeX and pdf formats

Identifying \(\displaystyle f=- 9 x - 7\) and \(\displaystyle g=\left(4 - 6 x\right) \left(6 - 6 x\right)\) and using the product rule with \(\displaystyle f=- 9 x - 7 \implies f'=-9\). This leaves g as \(\displaystyle g = \left(4 - 6 x\right) \left(6 - 6 x\right)\) which also requires the product rule. Pushing down in the new product rule \(\displaystyle f=6 - 6 x \implies f'=-6\) and \(\displaystyle g=4 - 6 x \implies g'=-6\). Popping up a level gives \(\displaystyle g'=(4 - 6 x)(-6)+(6 - 6 x)(-6)\)Popping up again (Back to the original problem) gives \(\displaystyle f'=(- 9 x - 7)(72 x - 60)+(\left(4 - 6 x\right) \left(6 - 6 x\right))(-9)=- 6 \left(4 - 6 x\right) \left(- 9 x - 7\right) + \left(6 - 6 x\right) \left(54 x - 36\right) + \left(6 - 6 x\right) \left(54 x + 42\right)\)

Download \(\LaTeX\)

\begin{question}Find the derivative of $y = (- 9 x - 7)(6 - 6 x)(4 - 6 x)$.
    \soln{9cm}{Identifying $f=- 9 x - 7$ and $g=\left(4 - 6 x\right) \left(6 - 6 x\right)$ and using the product rule with $f=- 9 x - 7 \implies f'=-9$. This leaves g as $g = \left(4 - 6 x\right) \left(6 - 6 x\right)$ which also requires the product rule. Pushing down in the new product rule $f=6 - 6 x \implies f'=-6$ and $g=4 - 6 x \implies g'=-6$. Popping up a level gives $g'=(4 - 6 x)(-6)+(6 - 6 x)(-6)$Popping up again (Back to the original problem) gives $f'=(- 9 x - 7)(72 x - 60)+(\left(4 - 6 x\right) \left(6 - 6 x\right))(-9)=- 6 \left(4 - 6 x\right) \left(- 9 x - 7\right) + \left(6 - 6 x\right) \left(54 x - 36\right) + \left(6 - 6 x\right) \left(54 x + 42\right)$}

\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 - 7)(6 - 6 x)(4 - 6 x) " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%20%28-%209%20x%20-%207%29%286%20-%206%20x%29%284%20-%206%20x%29%20" alt="LaTeX:  \displaystyle y = (- 9 x - 7)(6 - 6 x)(4 - 6 x) " data-equation-content=" \displaystyle y = (- 9 x - 7)(6 - 6 x)(4 - 6 x) " /> .</p> </p>

HTML for Canvas

<p> <p>Identifying  <img class="equation_image" title=" \displaystyle f=- 9 x - 7 " src="/equation_images/%20%5Cdisplaystyle%20f%3D-%209%20x%20-%207%20" alt="LaTeX:  \displaystyle f=- 9 x - 7 " data-equation-content=" \displaystyle f=- 9 x - 7 " />  and  <img class="equation_image" title=" \displaystyle g=\left(4 - 6 x\right) \left(6 - 6 x\right) " src="/equation_images/%20%5Cdisplaystyle%20g%3D%5Cleft%284%20-%206%20x%5Cright%29%20%5Cleft%286%20-%206%20x%5Cright%29%20" alt="LaTeX:  \displaystyle g=\left(4 - 6 x\right) \left(6 - 6 x\right) " data-equation-content=" \displaystyle g=\left(4 - 6 x\right) \left(6 - 6 x\right) " />  and using the product rule with  <img class="equation_image" title=" \displaystyle f=- 9 x - 7 \implies f'=-9 " src="/equation_images/%20%5Cdisplaystyle%20f%3D-%209%20x%20-%207%20%5Cimplies%20f%27%3D-9%20" alt="LaTeX:  \displaystyle f=- 9 x - 7 \implies f'=-9 " data-equation-content=" \displaystyle f=- 9 x - 7 \implies f'=-9 " /> . This leaves g as  <img class="equation_image" title=" \displaystyle g = \left(4 - 6 x\right) \left(6 - 6 x\right) " src="/equation_images/%20%5Cdisplaystyle%20g%20%3D%20%5Cleft%284%20-%206%20x%5Cright%29%20%5Cleft%286%20-%206%20x%5Cright%29%20" alt="LaTeX:  \displaystyle g = \left(4 - 6 x\right) \left(6 - 6 x\right) " data-equation-content=" \displaystyle g = \left(4 - 6 x\right) \left(6 - 6 x\right) " />  which also requires the product rule. Pushing down in the new product rule  <img class="equation_image" title=" \displaystyle f=6 - 6 x \implies f'=-6 " src="/equation_images/%20%5Cdisplaystyle%20f%3D6%20-%206%20x%20%5Cimplies%20f%27%3D-6%20" alt="LaTeX:  \displaystyle f=6 - 6 x \implies f'=-6 " data-equation-content=" \displaystyle f=6 - 6 x \implies f'=-6 " />  and  <img class="equation_image" title=" \displaystyle g=4 - 6 x \implies g'=-6 " src="/equation_images/%20%5Cdisplaystyle%20g%3D4%20-%206%20x%20%5Cimplies%20g%27%3D-6%20" alt="LaTeX:  \displaystyle g=4 - 6 x \implies g'=-6 " data-equation-content=" \displaystyle g=4 - 6 x \implies g'=-6 " /> . Popping up a level gives  <img class="equation_image" title=" \displaystyle g'=(4 - 6 x)(-6)+(6 - 6 x)(-6) " src="/equation_images/%20%5Cdisplaystyle%20g%27%3D%284%20-%206%20x%29%28-6%29%2B%286%20-%206%20x%29%28-6%29%20" alt="LaTeX:  \displaystyle g'=(4 - 6 x)(-6)+(6 - 6 x)(-6) " data-equation-content=" \displaystyle g'=(4 - 6 x)(-6)+(6 - 6 x)(-6) " /> Popping up again (Back to the original problem) gives  <img class="equation_image" title=" \displaystyle f'=(- 9 x - 7)(72 x - 60)+(\left(4 - 6 x\right) \left(6 - 6 x\right))(-9)=- 6 \left(4 - 6 x\right) \left(- 9 x - 7\right) + \left(6 - 6 x\right) \left(54 x - 36\right) + \left(6 - 6 x\right) \left(54 x + 42\right) " src="/equation_images/%20%5Cdisplaystyle%20f%27%3D%28-%209%20x%20-%207%29%2872%20x%20-%2060%29%2B%28%5Cleft%284%20-%206%20x%5Cright%29%20%5Cleft%286%20-%206%20x%5Cright%29%29%28-9%29%3D-%206%20%5Cleft%284%20-%206%20x%5Cright%29%20%5Cleft%28-%209%20x%20-%207%5Cright%29%20%2B%20%5Cleft%286%20-%206%20x%5Cright%29%20%5Cleft%2854%20x%20-%2036%5Cright%29%20%2B%20%5Cleft%286%20-%206%20x%5Cright%29%20%5Cleft%2854%20x%20%2B%2042%5Cright%29%20" alt="LaTeX:  \displaystyle f'=(- 9 x - 7)(72 x - 60)+(\left(4 - 6 x\right) \left(6 - 6 x\right))(-9)=- 6 \left(4 - 6 x\right) \left(- 9 x - 7\right) + \left(6 - 6 x\right) \left(54 x - 36\right) + \left(6 - 6 x\right) \left(54 x + 42\right) " data-equation-content=" \displaystyle f'=(- 9 x - 7)(72 x - 60)+(\left(4 - 6 x\right) \left(6 - 6 x\right))(-9)=- 6 \left(4 - 6 x\right) \left(- 9 x - 7\right) + \left(6 - 6 x\right) \left(54 x - 36\right) + \left(6 - 6 x\right) \left(54 x + 42\right) " /> </p> </p>