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Questions: Algebra BusinessCalculus
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Find the differential, \(\displaystyle dy\), of \(\displaystyle y = e^{\sin{\left(x \right)}}\).
The differential is given by \(\displaystyle dy = f'(x)dx\). Using the formula gives:\begin{equation*} dy = e^{\sin{\left(x \right)}} \cos{\left(x \right)}\,dx \end{equation*}
\begin{question}Find the differential, $dy$, of $y = e^{\sin{\left(x \right)}}$.
\soln{9cm}{The differential is given by $dy = f'(x)dx$. Using the formula gives:\begin{equation*} dy = e^{\sin{\left(x \right)}} \cos{\left(x \right)}\,dx \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 differential, <img class="equation_image" title=" \displaystyle dy " src="/equation_images/%20%5Cdisplaystyle%20dy%20" alt="LaTeX: \displaystyle dy " data-equation-content=" \displaystyle dy " /> , of <img class="equation_image" title=" \displaystyle y = e^{\sin{\left(x \right)}} " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%20e%5E%7B%5Csin%7B%5Cleft%28x%20%5Cright%29%7D%7D%20" alt="LaTeX: \displaystyle y = e^{\sin{\left(x \right)}} " data-equation-content=" \displaystyle y = e^{\sin{\left(x \right)}} " /> . </p> </p><p> <p>The differential is given by <img class="equation_image" title=" \displaystyle dy = f'(x)dx " src="/equation_images/%20%5Cdisplaystyle%20dy%20%3D%20f%27%28x%29dx%20" alt="LaTeX: \displaystyle dy = f'(x)dx " data-equation-content=" \displaystyle dy = f'(x)dx " /> . Using the formula gives: <img class="equation_image" title=" dy = e^{\sin{\left(x \right)}} \cos{\left(x \right)}\,dx " src="/equation_images/%20%20dy%20%3D%20e%5E%7B%5Csin%7B%5Cleft%28x%20%5Cright%29%7D%7D%20%5Ccos%7B%5Cleft%28x%20%5Cright%29%7D%5C%2Cdx%20%20" alt="LaTeX: dy = e^{\sin{\left(x \right)}} \cos{\left(x \right)}\,dx " data-equation-content=" dy = e^{\sin{\left(x \right)}} \cos{\left(x \right)}\,dx " /> </p> </p>