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Questions: Algebra BusinessCalculus

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Calculus
Derivatives
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Find the derivative of \(\displaystyle y = \left(- 3 x - 6\right) e^{x}\).

Using the product rule with \(\displaystyle f = e^{x}\), \(\displaystyle f' = e^{x}\), \(\displaystyle g = - 3 x - 6\), and \(\displaystyle g'= -3\) gives:
\begin{equation*} y' = (- 3 x - 6)(e^{x}) + (e^{x})(-3) = \left(- 3 x - 6\right) e^{x} - 3 e^{x} \end{equation*}

Download \(\LaTeX\) 

\begin{question}Find the derivative of $y = \left(- 3 x - 6\right) e^{x}$. 
    \soln{9cm}{Using the product rule with $f = e^{x}$, $f' = e^{x}$, $g = - 3 x - 6$, and $g'= -3$ gives:\newline 
 \begin{equation*} y' =  (- 3 x - 6)(e^{x}) + (e^{x})(-3) = \left(- 3 x - 6\right) e^{x} - 3 e^{x} \end{equation*}}

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Find the derivative of  <img class="equation_image" title=" \displaystyle y = \left(- 3 x - 6\right) e^{x} " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%20%5Cleft%28-%203%20x%20-%206%5Cright%29%20e%5E%7Bx%7D%20" alt="LaTeX:  \displaystyle y = \left(- 3 x - 6\right) e^{x} " data-equation-content=" \displaystyle y = \left(- 3 x - 6\right) e^{x} " /> . </p> </p>
HTML for Canvas
<p> <p>Using the product rule with  <img class="equation_image" title=" \displaystyle f = e^{x} " src="/equation_images/%20%5Cdisplaystyle%20f%20%3D%20e%5E%7Bx%7D%20" alt="LaTeX:  \displaystyle f = e^{x} " data-equation-content=" \displaystyle f = e^{x} " /> ,  <img class="equation_image" title=" \displaystyle f' = e^{x} " src="/equation_images/%20%5Cdisplaystyle%20f%27%20%3D%20e%5E%7Bx%7D%20" alt="LaTeX:  \displaystyle f' = e^{x} " data-equation-content=" \displaystyle f' = e^{x} " /> ,  <img class="equation_image" title=" \displaystyle g = - 3 x - 6 " src="/equation_images/%20%5Cdisplaystyle%20g%20%3D%20-%203%20x%20-%206%20" alt="LaTeX:  \displaystyle g = - 3 x - 6 " data-equation-content=" \displaystyle g = - 3 x - 6 " /> , and  <img class="equation_image" title=" \displaystyle g'= -3 " src="/equation_images/%20%5Cdisplaystyle%20g%27%3D%20-3%20" alt="LaTeX:  \displaystyle g'= -3 " data-equation-content=" \displaystyle g'= -3 " />  gives:<br> 
  <img class="equation_image" title="  y' =  (- 3 x - 6)(e^{x}) + (e^{x})(-3) = \left(- 3 x - 6\right) e^{x} - 3 e^{x}  " src="/equation_images/%20%20y%27%20%3D%20%20%28-%203%20x%20-%206%29%28e%5E%7Bx%7D%29%20%2B%20%28e%5E%7Bx%7D%29%28-3%29%20%3D%20%5Cleft%28-%203%20x%20-%206%5Cright%29%20e%5E%7Bx%7D%20-%203%20e%5E%7Bx%7D%20%20" alt="LaTeX:   y' =  (- 3 x - 6)(e^{x}) + (e^{x})(-3) = \left(- 3 x - 6\right) e^{x} - 3 e^{x}  " data-equation-content="  y' =  (- 3 x - 6)(e^{x}) + (e^{x})(-3) = \left(- 3 x - 6\right) e^{x} - 3 e^{x}  " /> </p> </p>