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Questions: Algebra BusinessCalculus
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Find the derivative of \(\displaystyle y = \left(3 - 4 x\right) \left(- 4 x - 4\right)\).
Using the product rule with \(\displaystyle f = 3 - 4 x\), \(\displaystyle f' = -4\), \(\displaystyle g = - 4 x - 4\), and \(\displaystyle g'= -4\) gives:
\begin{equation*} y' = (- 4 x - 4)(-4) + (3 - 4 x)(-4) = 32 x + 4 \end{equation*}
\begin{question}Find the derivative of $y = \left(3 - 4 x\right) \left(- 4 x - 4\right)$.
\soln{9cm}{Using the product rule with $f = 3 - 4 x$, $f' = -4$, $g = - 4 x - 4$, and $g'= -4$ gives:\newline
\begin{equation*} y' = (- 4 x - 4)(-4) + (3 - 4 x)(-4) = 32 x + 4 \end{equation*}}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Find the derivative of <img class="equation_image" title=" \displaystyle y = \left(3 - 4 x\right) \left(- 4 x - 4\right) " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%20%5Cleft%283%20-%204%20x%5Cright%29%20%5Cleft%28-%204%20x%20-%204%5Cright%29%20" alt="LaTeX: \displaystyle y = \left(3 - 4 x\right) \left(- 4 x - 4\right) " data-equation-content=" \displaystyle y = \left(3 - 4 x\right) \left(- 4 x - 4\right) " /> . </p> </p>
<p> <p>Using the product rule with <img class="equation_image" title=" \displaystyle f = 3 - 4 x " src="/equation_images/%20%5Cdisplaystyle%20f%20%3D%203%20-%204%20x%20" alt="LaTeX: \displaystyle f = 3 - 4 x " data-equation-content=" \displaystyle f = 3 - 4 x " /> , <img class="equation_image" title=" \displaystyle f' = -4 " src="/equation_images/%20%5Cdisplaystyle%20f%27%20%3D%20-4%20" alt="LaTeX: \displaystyle f' = -4 " data-equation-content=" \displaystyle f' = -4 " /> , <img class="equation_image" title=" \displaystyle g = - 4 x - 4 " src="/equation_images/%20%5Cdisplaystyle%20g%20%3D%20-%204%20x%20-%204%20" alt="LaTeX: \displaystyle g = - 4 x - 4 " data-equation-content=" \displaystyle g = - 4 x - 4 " /> , and <img class="equation_image" title=" \displaystyle g'= -4 " src="/equation_images/%20%5Cdisplaystyle%20g%27%3D%20-4%20" alt="LaTeX: \displaystyle g'= -4 " data-equation-content=" \displaystyle g'= -4 " /> gives:<br>
<img class="equation_image" title=" y' = (- 4 x - 4)(-4) + (3 - 4 x)(-4) = 32 x + 4 " src="/equation_images/%20%20y%27%20%3D%20%20%28-%204%20x%20-%204%29%28-4%29%20%2B%20%283%20-%204%20x%29%28-4%29%20%3D%2032%20x%20%2B%204%20%20" alt="LaTeX: y' = (- 4 x - 4)(-4) + (3 - 4 x)(-4) = 32 x + 4 " data-equation-content=" y' = (- 4 x - 4)(-4) + (3 - 4 x)(-4) = 32 x + 4 " /> </p> </p>