Generate Math Exams and Quizzes in LaTeX and pdf formats

Identifying \(\displaystyle f=- 2 x^{2} + 2 x - 7\) and \(\displaystyle g=\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right)\) and using the product rule with \(\displaystyle f=- 2 x^{2} + 2 x - 7 \implies f'=2 - 4 x\). This leaves g as \(\displaystyle g = \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right)\) which also requires the product rule. Pushing down in the new product rule \(\displaystyle f=5 x^{2} - 9 x - 4 \implies f'=10 x - 9\) and \(\displaystyle g=- 3 x^{2} + 8 x - 5 \implies g'=8 - 6 x\). Popping up a level gives \(\displaystyle g'=(- 3 x^{2} + 8 x - 5)(10 x - 9)+(5 x^{2} - 9 x - 4)(8 - 6 x)\)Popping up again (Back to the original problem) gives \(\displaystyle f'=(- 2 x^{2} + 2 x - 7)(\left(8 - 6 x\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right))+(\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right))(2 - 4 x)=\left(2 - 4 x\right) \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) + \left(8 - 6 x\right) \left(- 2 x^{2} + 2 x - 7\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right) \left(- 2 x^{2} + 2 x - 7\right)\)

Download \(\LaTeX\)

\begin{question}Find the derivative of $y = (- 2 x^{2} + 2 x - 7)(5 x^{2} - 9 x - 4)(- 3 x^{2} + 8 x - 5)$.
    \soln{9cm}{Identifying $f=- 2 x^{2} + 2 x - 7$ and $g=\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right)$ and using the product rule with $f=- 2 x^{2} + 2 x - 7 \implies f'=2 - 4 x$. This leaves g as $g = \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right)$ which also requires the product rule. Pushing down in the new product rule $f=5 x^{2} - 9 x - 4 \implies f'=10 x - 9$ and $g=- 3 x^{2} + 8 x - 5 \implies g'=8 - 6 x$. Popping up a level gives $g'=(- 3 x^{2} + 8 x - 5)(10 x - 9)+(5 x^{2} - 9 x - 4)(8 - 6 x)$Popping up again (Back to the original problem) gives $f'=(- 2 x^{2} + 2 x - 7)(\left(8 - 6 x\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right))+(\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right))(2 - 4 x)=\left(2 - 4 x\right) \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) + \left(8 - 6 x\right) \left(- 2 x^{2} + 2 x - 7\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right) \left(- 2 x^{2} + 2 x - 7\right)$}

\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 = (- 2 x^{2} + 2 x - 7)(5 x^{2} - 9 x - 4)(- 3 x^{2} + 8 x - 5) " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%20%28-%202%20x%5E%7B2%7D%20%2B%202%20x%20-%207%29%285%20x%5E%7B2%7D%20-%209%20x%20-%204%29%28-%203%20x%5E%7B2%7D%20%2B%208%20x%20-%205%29%20" alt="LaTeX:  \displaystyle y = (- 2 x^{2} + 2 x - 7)(5 x^{2} - 9 x - 4)(- 3 x^{2} + 8 x - 5) " data-equation-content=" \displaystyle y = (- 2 x^{2} + 2 x - 7)(5 x^{2} - 9 x - 4)(- 3 x^{2} + 8 x - 5) " /> .</p> </p>

HTML for Canvas

<p> <p>Identifying  <img class="equation_image" title=" \displaystyle f=- 2 x^{2} + 2 x - 7 " src="/equation_images/%20%5Cdisplaystyle%20f%3D-%202%20x%5E%7B2%7D%20%2B%202%20x%20-%207%20" alt="LaTeX:  \displaystyle f=- 2 x^{2} + 2 x - 7 " data-equation-content=" \displaystyle f=- 2 x^{2} + 2 x - 7 " />  and  <img class="equation_image" title=" \displaystyle g=\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) " src="/equation_images/%20%5Cdisplaystyle%20g%3D%5Cleft%28-%203%20x%5E%7B2%7D%20%2B%208%20x%20-%205%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20-%209%20x%20-%204%5Cright%29%20" alt="LaTeX:  \displaystyle g=\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) " data-equation-content=" \displaystyle g=\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) " />  and using the product rule with  <img class="equation_image" title=" \displaystyle f=- 2 x^{2} + 2 x - 7 \implies f'=2 - 4 x " src="/equation_images/%20%5Cdisplaystyle%20f%3D-%202%20x%5E%7B2%7D%20%2B%202%20x%20-%207%20%5Cimplies%20f%27%3D2%20-%204%20x%20" alt="LaTeX:  \displaystyle f=- 2 x^{2} + 2 x - 7 \implies f'=2 - 4 x " data-equation-content=" \displaystyle f=- 2 x^{2} + 2 x - 7 \implies f'=2 - 4 x " /> . This leaves g as  <img class="equation_image" title=" \displaystyle g = \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) " src="/equation_images/%20%5Cdisplaystyle%20g%20%3D%20%5Cleft%28-%203%20x%5E%7B2%7D%20%2B%208%20x%20-%205%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20-%209%20x%20-%204%5Cright%29%20" alt="LaTeX:  \displaystyle g = \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) " data-equation-content=" \displaystyle g = \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) " />  which also requires the product rule. Pushing down in the new product rule  <img class="equation_image" title=" \displaystyle f=5 x^{2} - 9 x - 4 \implies f'=10 x - 9 " src="/equation_images/%20%5Cdisplaystyle%20f%3D5%20x%5E%7B2%7D%20-%209%20x%20-%204%20%5Cimplies%20f%27%3D10%20x%20-%209%20" alt="LaTeX:  \displaystyle f=5 x^{2} - 9 x - 4 \implies f'=10 x - 9 " data-equation-content=" \displaystyle f=5 x^{2} - 9 x - 4 \implies f'=10 x - 9 " />  and  <img class="equation_image" title=" \displaystyle g=- 3 x^{2} + 8 x - 5 \implies g'=8 - 6 x " src="/equation_images/%20%5Cdisplaystyle%20g%3D-%203%20x%5E%7B2%7D%20%2B%208%20x%20-%205%20%5Cimplies%20g%27%3D8%20-%206%20x%20" alt="LaTeX:  \displaystyle g=- 3 x^{2} + 8 x - 5 \implies g'=8 - 6 x " data-equation-content=" \displaystyle g=- 3 x^{2} + 8 x - 5 \implies g'=8 - 6 x " /> . Popping up a level gives  <img class="equation_image" title=" \displaystyle g'=(- 3 x^{2} + 8 x - 5)(10 x - 9)+(5 x^{2} - 9 x - 4)(8 - 6 x) " src="/equation_images/%20%5Cdisplaystyle%20g%27%3D%28-%203%20x%5E%7B2%7D%20%2B%208%20x%20-%205%29%2810%20x%20-%209%29%2B%285%20x%5E%7B2%7D%20-%209%20x%20-%204%29%288%20-%206%20x%29%20" alt="LaTeX:  \displaystyle g'=(- 3 x^{2} + 8 x - 5)(10 x - 9)+(5 x^{2} - 9 x - 4)(8 - 6 x) " data-equation-content=" \displaystyle g'=(- 3 x^{2} + 8 x - 5)(10 x - 9)+(5 x^{2} - 9 x - 4)(8 - 6 x) " /> Popping up again (Back to the original problem) gives  <img class="equation_image" title=" \displaystyle f'=(- 2 x^{2} + 2 x - 7)(\left(8 - 6 x\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right))+(\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right))(2 - 4 x)=\left(2 - 4 x\right) \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) + \left(8 - 6 x\right) \left(- 2 x^{2} + 2 x - 7\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right) \left(- 2 x^{2} + 2 x - 7\right) " src="/equation_images/%20%5Cdisplaystyle%20f%27%3D%28-%202%20x%5E%7B2%7D%20%2B%202%20x%20-%207%29%28%5Cleft%288%20-%206%20x%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20-%209%20x%20-%204%5Cright%29%20%2B%20%5Cleft%2810%20x%20-%209%5Cright%29%20%5Cleft%28-%203%20x%5E%7B2%7D%20%2B%208%20x%20-%205%5Cright%29%29%2B%28%5Cleft%28-%203%20x%5E%7B2%7D%20%2B%208%20x%20-%205%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20-%209%20x%20-%204%5Cright%29%29%282%20-%204%20x%29%3D%5Cleft%282%20-%204%20x%5Cright%29%20%5Cleft%28-%203%20x%5E%7B2%7D%20%2B%208%20x%20-%205%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20-%209%20x%20-%204%5Cright%29%20%2B%20%5Cleft%288%20-%206%20x%5Cright%29%20%5Cleft%28-%202%20x%5E%7B2%7D%20%2B%202%20x%20-%207%5Cright%29%20%5Cleft%285%20x%5E%7B2%7D%20-%209%20x%20-%204%5Cright%29%20%2B%20%5Cleft%2810%20x%20-%209%5Cright%29%20%5Cleft%28-%203%20x%5E%7B2%7D%20%2B%208%20x%20-%205%5Cright%29%20%5Cleft%28-%202%20x%5E%7B2%7D%20%2B%202%20x%20-%207%5Cright%29%20" alt="LaTeX:  \displaystyle f'=(- 2 x^{2} + 2 x - 7)(\left(8 - 6 x\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right))+(\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right))(2 - 4 x)=\left(2 - 4 x\right) \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) + \left(8 - 6 x\right) \left(- 2 x^{2} + 2 x - 7\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right) \left(- 2 x^{2} + 2 x - 7\right) " data-equation-content=" \displaystyle f'=(- 2 x^{2} + 2 x - 7)(\left(8 - 6 x\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right))+(\left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right))(2 - 4 x)=\left(2 - 4 x\right) \left(- 3 x^{2} + 8 x - 5\right) \left(5 x^{2} - 9 x - 4\right) + \left(8 - 6 x\right) \left(- 2 x^{2} + 2 x - 7\right) \left(5 x^{2} - 9 x - 4\right) + \left(10 x - 9\right) \left(- 3 x^{2} + 8 x - 5\right) \left(- 2 x^{2} + 2 x - 7\right) " /> </p> </p>