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\lhead{\color{blue} \Large Lecture Notes}
\lfoot{\small   \copyright $\;$ copyright  Hidegkuti,  Powell,  2014}
\rfoot{\small   Last revised:  February 25, 2014}
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\chead{\LARGE Differentiation - Practice}
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\begin{document}


Differentiate each of the following functions.\bigskip

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\begin{enumerate}
\item $f\left( x\right) =\sqrt{x}\cos x$\medskip

\item $f\left( x\right) =x^{3}\sin x$\medskip

\item $f\left( x\right) =\sqrt[3]{x^{5}}\sin x$\medskip

\item $f\left( x\right) =\left( 3x^{8}-x^{6}\right) \sin x$\medskip

\item $f\left( x\right) =\sin 2x$\medskip

\item $f\left( x\right) =\dfrac{\sin x+\cos x}{x^{3}}$\medskip

\item $f\left( x\right) =\left( 3\cos x-\sin x\right) \sqrt{x}$\medskip

\item $f\left( x\right) =\left( x^{3}-5x^{2}+1\right) \sin x$\medskip

\item $f\left( x\right) =\dfrac{\sin x}{x}+x^{3}\cos x$\medskip

\item $f\left( x\right) =\left( \cos x\right) \left( x^{2}-4x+1\right) $%
\medskip
\end{enumerate}

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\begin{center}
{\Large Answers}\bigskip \bigskip
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1.) \ $f^{\prime }\left( x\right) =\dfrac{1}{2\sqrt{x}}\cos x-\sqrt{x}\sin x$
\ \ \ \ \ \ 2.) $\ f^{\prime }\left( x\right) =x^{3}\cos x+3x^{2}\sin x$%
\bigskip\ \ \ \ 

3.) \ $f^{\prime }\left( x\right) =\left( \cos x\right) \sqrt[3]{x^{5}}+%
\dfrac{5}{3}\sqrt[3]{x^{2}}\left( \sin x\right) $ \ \ \ 4.) \ \ $f^{\prime
}\left( x\right) =\allowbreak \left( \cos x\right) \left(
3x^{8}-x^{6}\right) +\left( \sin x\right) \left( 24x^{7}-6x^{5}\right) $%
\bigskip

5.) \ \ $f^{\prime }\left( x\right) =2\left( \cos ^{2}x-\sin ^{2}x\right)
=2\cos 2x$ \ \ \ \ \ \ \ \ \ 6.) \ $f^{\prime }\left( x\right) =\allowbreak 
\dfrac{1}{x^{3}}\left( \cos x-\sin x\right) -\dfrac{3}{x^{4}}\left( \cos
x+\sin x\right) $\ \bigskip

7.)\ \ $f^{\prime }\left( x\right) =\allowbreak \dfrac{1}{2\sqrt{x}}\left(
3\cos x-\sin x\right) +\sqrt{x}\left( -\cos x-3\sin x\right) \allowbreak $ \
\ \ \ \ \bigskip

8.) \ $f^{\prime }\left( x\right) =\allowbreak \sin x\left(
3x^{2}-10x\right) +\cos x\left( x^{3}-5x^{2}+1\right) $\bigskip

9.) \ $f^{\prime }\left( x\right) =\allowbreak \dfrac{1}{x}\cos x+3x^{2}\cos
x-\dfrac{1}{x^{2}}\sin x-x^{3}\sin x$ \ \ \ \ \ \ \ \ \bigskip

10.) \ \ $f^{\prime }\left( x\right) =\allowbreak \left( \cos x\right)
\left( 2x-4\right) -\left( \sin x\right) \left( x^{2}-4x+1\right)
\allowbreak $\bigskip

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\href{https://teaching.martahidegkuti.com/shared/lnotes/lecturenotes.html}{%
For more documents like this, visit our page at\
https://teaching.martahidegkuti.com and click on Lecture Notes. \ E-mail
questions or comments to mhidegkuti@ccc.edu.}

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