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Questions: Algebra BusinessCalculus
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Find the derivative
The solution goes here.
\begin{question}Find the derivative
\begin{enumerate}
\item (10pts) $f(x) = \frac{1}{2 \sqrt{x}}$
\soln{4cm}{
$f'(x)=- \frac{1}{4 x^{\frac{3}{2}}}$
}
\item (10pts) $f(x) = \sqrt{x}$
\soln{4cm}{
$f'(x)=\frac{1}{2 \sqrt{x}}$
}
\item (10pts) $f(x) = x^{2}$
\soln{4cm}{
$f'(x)=2 x$
}
\item (10pts) $f(x) = - \cos{\left(x \right)}$
\soln{4cm}{
$f'(x)=\sin{\left(x \right)}$
}
\end{enumerate}
\soln{9cm}{The solution goes here.}
\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
<ol type="a">
<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) = \sqrt{x} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20%5Csqrt%7Bx%7D%20" alt="LaTeX: \displaystyle f(x) = \sqrt{x} " data-equation-content=" \displaystyle f(x) = \sqrt{x} " /> </li>
<li> <img class="equation_image" title=" \displaystyle f(x) = x^{2} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20x%5E%7B2%7D%20" alt="LaTeX: \displaystyle f(x) = x^{2} " data-equation-content=" \displaystyle f(x) = x^{2} " /> </li>
<li> <img class="equation_image" title=" \displaystyle f(x) = - \cos{\left(x \right)} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20-%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><p> <p>The solution goes here.
<ol type="a">
<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)=\frac{1}{2 \sqrt{x}} " src="/equation_images/%20%5Cdisplaystyle%20f%27%28x%29%3D%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)=2 x " src="/equation_images/%20%5Cdisplaystyle%20f%27%28x%29%3D2%20x%20" alt="LaTeX: \displaystyle f'(x)=2 x " data-equation-content=" \displaystyle f'(x)=2 x " /> </li>
<li> <img class="equation_image" title=" \displaystyle f'(x)=\sin{\left(x \right)} " src="/equation_images/%20%5Cdisplaystyle%20f%27%28x%29%3D%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>