\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Find the differential, \(\displaystyle dy\), of \(\displaystyle y = e^{\sin{\left(7 x \right)}}\).
The differential is given by \(\displaystyle dy = f'(x)dx\). Using the formula gives:\begin{equation*} dy = 7 e^{\sin{\left(7 x \right)}} \cos{\left(7 x \right)}\,dx \end{equation*}
\begin{question}Find the differential, $dy$, of $y = e^{\sin{\left(7 x \right)}}$.
\soln{9cm}{The differential is given by $dy = f'(x)dx$. Using the formula gives:\begin{equation*} dy = 7 e^{\sin{\left(7 x \right)}} \cos{\left(7 x \right)}\,dx \end{equation*}}
\end{question}
\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}<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(7 x \right)}} " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%20e%5E%7B%5Csin%7B%5Cleft%287%20x%20%5Cright%29%7D%7D%20" alt="LaTeX: \displaystyle y = e^{\sin{\left(7 x \right)}} " data-equation-content=" \displaystyle y = e^{\sin{\left(7 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 = 7 e^{\sin{\left(7 x \right)}} \cos{\left(7 x \right)}\,dx " src="/equation_images/%20%20dy%20%3D%207%20e%5E%7B%5Csin%7B%5Cleft%287%20x%20%5Cright%29%7D%7D%20%5Ccos%7B%5Cleft%287%20x%20%5Cright%29%7D%5C%2Cdx%20%20" alt="LaTeX: dy = 7 e^{\sin{\left(7 x \right)}} \cos{\left(7 x \right)}\,dx " data-equation-content=" dy = 7 e^{\sin{\left(7 x \right)}} \cos{\left(7 x \right)}\,dx " /> </p> </p>