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Questions: Algebra BusinessCalculus

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Calculus
Derivatives
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Find the derivative

  1. \(\displaystyle f(x) = e^{x}\)
  2. \(\displaystyle f(x) = \frac{1}{x}\)
  3. \(\displaystyle f(x) = \frac{1}{2 \sqrt{x}}\)
  4. \(\displaystyle f(x) = - \sin{\left(x \right)}\)

The solution goes here.

  1. \(\displaystyle f'(x)=e^{x}\)
  2. \(\displaystyle f'(x)=- \frac{1}{x^{2}}\)
  3. \(\displaystyle f'(x)=- \frac{1}{4 x^{\frac{3}{2}}}\)
  4. \(\displaystyle f'(x)=- \cos{\left(x \right)}\)

Download \(\LaTeX\) 

\begin{question}Find the derivative
\begin{enumerate}
    \item (10pts) $f(x) = e^{x}$
        \soln{4cm}{
            $f'(x)=e^{x}$ 
        }
    \item (10pts) $f(x) = \frac{1}{x}$
        \soln{4cm}{
            $f'(x)=- \frac{1}{x^{2}}$ 
        }
    \item (10pts) $f(x) = \frac{1}{2 \sqrt{x}}$
        \soln{4cm}{
            $f'(x)=- \frac{1}{4 x^{\frac{3}{2}}}$ 
        }
    \item (10pts) $f(x) = - \sin{\left(x \right)}$
        \soln{4cm}{
            $f'(x)=- \cos{\left(x \right)}$ 
        }
\end{enumerate}
    \soln{9cm}{The solution goes here.}

\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
<ol type="a">
	<li> <img class="equation_image" title=" \displaystyle f(x) = e^{x} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20e%5E%7Bx%7D%20" alt="LaTeX:  \displaystyle f(x) = e^{x} " data-equation-content=" \displaystyle f(x) = e^{x} " /> </li>
	<li> <img class="equation_image" title=" \displaystyle f(x) = \frac{1}{x} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20" alt="LaTeX:  \displaystyle f(x) = \frac{1}{x} " data-equation-content=" \displaystyle f(x) = \frac{1}{x} " /> </li>
	<li> <img class="equation_image" title=" \displaystyle f(x) = \frac{1}{2 \sqrt{x}} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2%20%5Csqrt%7Bx%7D%7D%20" alt="LaTeX:  \displaystyle f(x) = \frac{1}{2 \sqrt{x}} " data-equation-content=" \displaystyle f(x) = \frac{1}{2 \sqrt{x}} " /> </li>
	<li> <img class="equation_image" title=" \displaystyle f(x) = - \sin{\left(x \right)} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20-%20%5Csin%7B%5Cleft%28x%20%5Cright%29%7D%20" alt="LaTeX:  \displaystyle f(x) = - \sin{\left(x \right)} " data-equation-content=" \displaystyle f(x) = - \sin{\left(x \right)} " /> </li>

</ol>
</p> </p>
HTML for Canvas
<p> <p>The solution goes here.
<ol type="a">
	<li> <img class="equation_image" title=" \displaystyle f'(x)=e^{x} " src="/equation_images/%20%5Cdisplaystyle%20f%27%28x%29%3De%5E%7Bx%7D%20" alt="LaTeX:  \displaystyle f'(x)=e^{x} " data-equation-content=" \displaystyle f'(x)=e^{x} " /> </li>
	<li> <img class="equation_image" title=" \displaystyle f'(x)=- \frac{1}{x^{2}} " src="/equation_images/%20%5Cdisplaystyle%20f%27%28x%29%3D-%20%5Cfrac%7B1%7D%7Bx%5E%7B2%7D%7D%20" alt="LaTeX:  \displaystyle f'(x)=- \frac{1}{x^{2}} " data-equation-content=" \displaystyle f'(x)=- \frac{1}{x^{2}} " /> </li>
	<li> <img class="equation_image" title=" \displaystyle f'(x)=- \frac{1}{4 x^{\frac{3}{2}}} " src="/equation_images/%20%5Cdisplaystyle%20f%27%28x%29%3D-%20%5Cfrac%7B1%7D%7B4%20x%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20" alt="LaTeX:  \displaystyle f'(x)=- \frac{1}{4 x^{\frac{3}{2}}} " data-equation-content=" \displaystyle f'(x)=- \frac{1}{4 x^{\frac{3}{2}}} " /> </li>
	<li> <img class="equation_image" title=" \displaystyle f'(x)=- \cos{\left(x \right)} " src="/equation_images/%20%5Cdisplaystyle%20f%27%28x%29%3D-%20%5Ccos%7B%5Cleft%28x%20%5Cright%29%7D%20" alt="LaTeX:  \displaystyle f'(x)=- \cos{\left(x \right)} " data-equation-content=" \displaystyle f'(x)=- \cos{\left(x \right)} " /> </li>
</ol></p> </p>