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\noindent
\parbox{1.5in}{\bf Math 1110}
\hfill {\Large \bf Formulas and Supplemental Exercises} \hfill
\parbox{1.5in}{\bf \hfill Derivatives Practice}

\vspace{0.2in}

\noindent {\bf\large Formulas and rules\dots}

\vspace{-0.15in}

\[ \mbox{Linearity:} \quad \dfrac{d}{dx}\Bigg[ f(x)+g(x) \Bigg] = f'(x)+g'(x)   \quad \mbox{and} \quad \dfrac{d}{dx}\Bigg[ c\,f(x) \Bigg] = c\,f'(x)  \qquad \qquad
    \dfrac{d}{dx}\Bigg[ mx+b \Bigg] =m \qquad \dfrac{d}{dx}\Bigg[ c \Bigg]  =0 \]

\[ \mbox{Power rule:} \quad \dfrac{d}{dx}\Bigg[ x^n \Bigg] = nx^{n-1} \qquad \qquad \dfrac{d}{dx}\Bigg[ b^x \Bigg] = b^x \,\ln(b) \qquad
    \dfrac{d}{dx}\Bigg[ e^x \Bigg] = e^x \qquad \dfrac{d}{dx}\Bigg[ \ln|x| \Bigg] = \dfrac{1}{x} \]

\[ \mbox{Product rule:} \quad \dfrac{d}{dx}\Bigg[ f(x)g(x) \Bigg] = f'(x)g(x)+f(x)g'(x)  \qquad \qquad
    \mbox{Quotient rule:} \quad \dfrac{d}{dx}\Bigg[ \dfrac{f(x)}{g(x)} \Bigg] = \dfrac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}  \]

\[ \mbox{Chain rule:} \quad \dfrac{d}{dx}\Bigg[ f(g(x)) \Bigg] = f'(g(x))\,g'(x) \qquad \qquad
    \dfrac{d}{dx}\Bigg[ \sin(x) \Bigg] = \cos(x) \qquad
    \dfrac{d}{dx}\Bigg[ \cos(x) \Bigg] = -\sin(x)  \] 

\[ \dfrac{d}{dx}\Bigg[ \tan(x) \Bigg] = \sec^2(x) \qquad
   \dfrac{d}{dx}\Bigg[ \sec(x) \Bigg] = \sec(x)\tan(x) \qquad
    \dfrac{d}{dx}\Bigg[ \cot(x) \Bigg] = -\csc^2(x) \qquad
    \dfrac{d}{dx}\Bigg[ \csc(x) \Bigg] = -\csc(x)\cot(x) \]

\[ \dfrac{d}{dx}\Bigg[ \arcsin(x) \Bigg] = \dfrac{1}{\sqrt{1-x^2}} \qquad
    \dfrac{d}{dx}\Bigg[ \arccos(x) \Bigg] = -\dfrac{1}{\sqrt{1-x^2}} \qquad
    \dfrac{d}{dx}\Bigg[ \arctan(x) \Bigg] = \dfrac{1}{1+x^2} 
\]

\[ \dfrac{d}{dx}\Bigg[ \sinh(x) \Bigg] = \cosh(x) \qquad
    \dfrac{d}{dx}\Bigg[ \cosh(x) \Bigg] = \sinh(x) 
\]

\vspace{0.1in}

\noindent {\bf\large For completeness (but you don't need to know these)\dots}\footnote{The derivatives of arcsecant and arccosecant do not match our text's formulas. This is because there are two competing conventions for defining these functions. These formulas go with the standard convention. Our textbook's non-standard convention yields derivative formulas with absolute values appearing.}

\[ \dfrac{d}{dx}\Bigg[ \mathrm{arcsec}(x) \Bigg] = \dfrac{1}{|x|\sqrt{x^2-1}} \qquad 
    \dfrac{d}{dx}\Bigg[ \mathrm{arccsc}(x) \Bigg] = -\dfrac{1}{|x|\sqrt{x^2-1}} \qquad
    \dfrac{d}{dx}\Bigg[ \mathrm{arccot}(x) \Bigg] = -\dfrac{1}{1+x^2}  \]

\[ \dfrac{d}{dx}\Bigg[ \mathrm{tanh}(x) \Bigg] = \mathrm{sech}^2(x) \quad
    \dfrac{d}{dx}\Bigg[ \mathrm{sech}(x) \Bigg] = -\mathrm{sech}(x)\mathrm{tanh}(x) \quad
    \dfrac{d}{dx}\Bigg[ \mathrm{coth}(x) \Bigg] = -\mathrm{csch}^2(x) \quad
    \dfrac{d}{dx}\Bigg[ \mathrm{csch}(x) \Bigg] = -\mathrm{csch}(x)\mathrm{coth}(x) \]

\[ \dfrac{d}{dx}\Bigg[ \mathrm{arcsinh}(x) \Bigg] = \dfrac{1}{\sqrt{x^2+1}} \qquad
    \dfrac{d}{dx}\Bigg[ \mathrm{arccosh}(x) \Bigg] = \dfrac{1}{\sqrt{x^2-1}} \qquad
    \dfrac{d}{dx}\Bigg[ \mathrm{arctanh}(x) \Bigg] = \dfrac{1}{1-x^2} \]

\[ \dfrac{d}{dx}\Bigg[ \mathrm{arcsech}(x) \Bigg] = -\dfrac{1}{x\sqrt{1-x^2}} \qquad
    \dfrac{d}{dx}\Bigg[ \mathrm{arccsch}(x) \Bigg] = -\dfrac{1}{|x|\sqrt{x^2+1}} \qquad
    \dfrac{d}{dx}\Bigg[ \mathrm{arccoth}(x) \Bigg] = \dfrac{1}{1-x^2} \]

\vspace{0.15in}

\noindent {\bf\large A Bit about Technology\dots}

\vspace{0.05in}

This sheet contains a list of practice problems along with links to solutions generated by Wolfram Alpha and SymboLab. 

\vspace{0.05in}

There are several major computer algebra systems (CASs for short). Many of our undergraduate math classes use a system called Maple. Another major CAS is Mathematica. Mathematica is part of what powers the online computational engine known as Wolfram Alpha. We have used several demos powered by the SageMath CAS. While SAGE's user interface is not as polished as those of Maple and Mathematica, it is open source and free to use. Even Wolfram Alpha, while available freely, has locked featured behind its paywall.
Other popular online tools are Desmos which creates beautiful graphs (but does not do symbolic calculations) and SymboLab which does various mathematical computations. 

\vspace{0.05in}

SymboLab is much more limited than the CASs mentioned above, but it has an easy user interface and provides step-by-step solutions for some basic problems in algebra and calculus. This includes including step-by-step derivative calculations. If you're still having trouble with derivative rules, I think you'll find SymboLab to be very helpful.

\vspace{0.05in}

It is also worth mentioning that SAGE, Desmos, Wolfram Alpha, and SymboLab are all available for free via a web browser. Some of these have accompanying smartphone apps (which generally are not free). For example, Desmos is free while Alpha's is a few dollars. SymboLab's app is free but has locked features which require a payment to unlock. Personally, I'd just access these tools via a browser. 

\begin{itemize}

\item Maple (a powerful CAS used in many classes at AppState): \href{https://www.maplesoft.com}{https://www.maplesoft.com}
\item Mathematica (a powerful CAS and the machine behind Wolfram Alpha): \href{https://www.wolfram.com/mathematica/}{https://www.wolfram.com/mathematica/}
\item SAGE (an open source CAS which powers many demos used in our class): \href{http://www.sagemath.org}{http://www.sagemath.org}
\item Wolfram Alpha (a mostly free online computational engine): \href{http://www.WolframAlpha.com}{http://www.wolframalpha.com}
\item SymboLab (a free online algebra and calculus calculator): \href{https://www.symbolab.com}{https://www.symbolab.com}
\item Desmos (a free online graphing utility): \href{https://www.desmos.com}{https://www.desmos.com}
\end{itemize}

\vspace{0.05in}

\noindent {\bf\large Problems\dots}

Compute the derivative. These problems begin with ``basics'' and then start adding rules and new functions. The problems toward the end are generally trickier than those at the beginning.

\vspace{0.05in}

Try some basic simplification as well. Being able to simplify answers is important in many contexts -- that said -- simplification is not the focus of this exercise so don't waste a lot of time fighting with algebra.

\vspace{0.05in}

\noindent {\it Note:} Clicking on ``\ALPHA{}'' will take you Wolfram Alpha's solution, and clicking on ``\SYMBO{}'' will take you to SymboLab's solution.

%\vspace{0.1in}

\begin{multicols}{2}
\begin{enumerate}
\item \myEx{y=\sqrt[3]{x}+\dfrac{1}{x}-\ln(x)+7x}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+x%5E(1%2F3)%2B1%2Fx-ln(x)%2B7x}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(x%5E%7B%5Cleft(1%2F3%5Cright)%7D%2B1%2Fx-ln%5Cleft(x%5Cright)%2B7x%5Cright)}{\SYMBO} 

\item \myEx{y=\dfrac{3x^2-\sqrt{x}}{x^5}+\pi^{10}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+(3x%5E2-sqrt(x))%2F(x%5E5)+%2B+pi%5E10}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%5Cleft(3x%5E%7B2%7D-sqrt%5Cleft(x%5Cright)%5Cright)%2F%5Cleft(x%5E%7B5%7D%5Cright)%20%2B%20pi%5E%7B10%7D%5Cright)}{\SYMBO} 

\item \myEx{y=3^x(x^5+9x-1)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+3%5Ex(x%5E5%2B9x-1)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(3%5E%7Bx%7D%5Cleft(x%5E%7B5%7D%2B9x-1%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\dfrac{x^2+3x}{3x^2-2x+1}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+(x%5E2%2B3x)%2F(3x%5E2-2x%2B1)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%5Cleft(x%5E%7B2%7D%2B3x%5Cright)%2F%5Cleft(3x%5E%7B2%7D-2x%2B1%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\dfrac{e^x+2x-1}{5x^3+x^2-12}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+(e%5Ex%2B2x-1)%2F(5x%5E3%2Bx%5E2-12)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%5Cleft(e%5E%7Bx%7D%2B2x-1%5Cright)%2F%5Cleft(5x%5E%7B3%7D%2Bx%5E%7B2%7D-12%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=e^{2x}(x^3+6x-1)\ln(x)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+e%5E(2x)(x%5E3%2B6x-1)ln(x)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(e%5E%7B%5Cleft(2x%5Cright)%7D%5Cleft(x%5E%7B3%7D%2B6x-1%5Cright)ln%5Cleft(x%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=x^5\sin(3x)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+x%5E5+sin(3x)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(x%5E%7B5%7D%20sin%5Cleft(3x%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\dfrac{1}{\sqrt{x^6-5x^4+x^3-2}}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+1%2F(sqrt(x%5E6-5x%5E4%2Bx%5E3-2))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%201%2F%5Cleft(sqrt%5Cleft(x%5E%7B6%7D-5x%5E%7B4%7D%2Bx%5E%7B3%7D-2%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=(x^2+\cos(x))^5}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+(x%5E2%2Bcos(x))%5E5}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%5Cleft(x%5E%7B2%7D%2Bcos%5Cleft(x%5Cright)%5Cright)%5E%7B5%7D%5Cright)}{\SYMBO} 

\item \myEx{y=99^{\mathrm{arctan}(x)}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+99%5Earctan(x)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(99%5E%7B%5Carctan%5Cleft(x%5Cright)%7D%5Cright)}{\SYMBO} 

\item \myEx{y=x\sinh(x^2)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+x+sinh(x%5E2)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%20x%20sinh%5Cleft(x%5E%7B2%7D%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=e^{x^2\sin(8x)}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+e%5E(x%5E2+sin(8x))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%20e%5E%7B%5Cleft(x%5E2%20sin%5Cleft(8x%5Cright)%5Cright)%7D%5Cright)}{\SYMBO} 

\item \myEx{y=\sinh^3(x)\sin^2(x)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+sinh%5E3(x)+sin%5E2(x)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%20sinh%5E%7B3%7D%5Cleft(x%5Cright)%20sin%5E%7B2%7D%5Cleft(x%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\tan\left(\dfrac{x}{x+1}\right)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+tan(x%2F(x%2B1))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%20tan%5Cleft(x%2F%5Cleft(x%2B1%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y= \dfrac{1+\csc(x^2)}{1-\cot(x^2)}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+(1%2Bcsc(x%5E2))%2F(1-cot(x%5E2))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%20%5Cleft(1%2Bcsc%5Cleft(x%5E%7B2%7D%5Cright)%5Cright)%2F%5Cleft(1-cot%5Cleft(x%5E%7B2%7D%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\tan^5(x^3)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+tan%5E5(x%5E3)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%20tan%5E%7B5%7D%5Cleft(x%5E%7B3%7D%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\dfrac{\sec(9x)+1}{x^3e^{-x}}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+(sec(9x)%2B1)%2F(x%5E3e%5E(-x))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%5Cleft(sec%5Cleft(9x%5Cright)%2B1%5Cright)%2F%5Cleft(x%5E%7B3%7De%5E%7B%5Cleft(-x%5Cright)%7D%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\ln(\arcsin(x)+1)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+ln(arcsin(x)%2B1)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(ln%5Cleft(arcsin%5Cleft(x%5Cright)%2B1%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\dfrac{\sin(x^3)+2x-1}{\mathrm{arctan}(x)}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+(sin(x%5E3)%2B2x-1)%2Farctan(x)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%5Cleft(sin%5Cleft(x%5E%7B3%7D%5Cright)%2B2x-1%5Cright)%2Farctan%5Cleft(x%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\sqrt{x^{6}+e^{4x}+\sinh(5x+1)}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+sqrt(x%5E6%2Be%5E(4x)%2Bsinh(5x%2B1))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(sqrt%5Cleft(x%5E%7B6%7D%2Be%5E%7B%5Cleft(4x%5Cright)%7D%2Bsinh%5Cleft(5x%2B1%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\cosh\left(\dfrac{x^2+1}{e^{7x}}\right)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+cosh((x%5E2%2B1)%2F(e%5E(7x)))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(cosh%5Cleft(%5Cleft(x%5E%7B2%7D%2B1%5Cright)%2F%5Cleft(e%5E%7B%5Cleft(7x%5Cright)%7D%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\sec(\ln(\mathrm{arcsin}(5^x)))}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+sec(ln(arcsin(5%5Ex)))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(sec%5Cleft(ln%5Cleft(arcsin%5Cleft(5%5E%7Bx%7D%5Cright)%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\tan\left(\dfrac{5}{x}\right)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+tan(5%2Fx)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%20tan%5Cleft(5%2Fx%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\ln\left(\dfrac{\sqrt[3]{7x^5+2x+1}}{x^{10}e^x}\right)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+ln(((7x%5E5%2B2x%2B1)%5E(1%2F3))%2F(x%5E(10)e%5Ex))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(ln%5Cleft(%5Cleft(%5Cleft(7x%5E%7B5%7D%2B2x%2B1%5Cright)%5E%7B%5Cleft(1%2F3%5Cright)%7D%5Cright)%2F%5Cleft(x%5E%7B%5Cleft(10%5Cright)%7De%5E%7Bx%7D%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\ln\left(\dfrac{x^9(x^2+1)}{e^{3x+2}\sqrt{x}}\right)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+ln((x%5E9(x%5E2%2B1))%2F(e%5E(3x%2B2)sqrt(x)))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(ln%5Cleft(%5Cleft(x%5E%7B9%7D%5Cleft(x%5E%7B2%7D%2B1%5Cright)%5Cright)%2F%5Cleft(e%5E%7B%5Cleft(3x%2B2%5Cright)%7Dsqrt%5Cleft(x%5Cright)%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\csc(5x)\,\mathrm{arccos}(x^3)}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+csc(5x)+arccos(x%5E3)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(csc%5Cleft(5x%5Cright)%20arccos%5Cleft(x%5E%7B3%7D%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\ln(x^7\sin(3x))}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+ln(x%5E7+sin(3x))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(ln%5Cleft(x%5E%7B7%7D%20sin%5Cleft(3x%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\cos(\cot(\sqrt{1+x^2}))}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+cos(cot(sqrt(1%2Bx%5E2)))}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%20cos%5Cleft(cot%5Cleft(sqrt%5Cleft(1%2Bx%5E%7B2%7D%5Cright)%5Cright)%5Cright)%5Cright)}{\SYMBO} 

\item \myEx{y=\sqrt[3]{x^2\ln(x^{55})}}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+(x%5E2+ln(x%5E(55)))%5E(1%2F3)}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%20%5Cleft(x%5E%7B2%7D%20ln%5Cleft(x%5E%7B%5Cleft(55%5Cright)%7D%5Cright)%5Cright)%5E%7B%5Cleft(1%2F3%5Cright)%7D%5Cright)}{\SYMBO} 

\item \myEx{y=(\csc(2x)+\sec(3x))^5}\;\;
         \href{http://www.wolframalpha.com/input/?i=derivative+(csc(2x)%2Bsec(3x))%5E5}{\ALPHA}\;\;
         \href{https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%5Cleft(csc%5Cleft(2x%5Cright)%2Bsec%5Cleft(3x%5Cright)%5Cright)%5E%7B5%7D%5Cright)}{\SYMBO} 

\end{enumerate}
\end{multicols}

\vfill

\end{document}

Answers:
\begin{multicols}{3}
\begin{enumerate}
\item $\lim\limits_{x \to 3} \dfrac{x-3}{3x^2-13x+12}=1/5$
\item $\lim\limits_{x \to 0} \dfrac{2\cosh(x)-2}{1-\cos(2x)}=1/2$
\item $\lim\limits_{x \to 0} \dfrac{x-\mathrm{arctan}(x)}{x^3}=1/3$
\item $\lim\limits_{x \to 0} \dfrac{x+\tan(x)}{\sin(x)}=2$ 
\item $\lim\limits_{t \to 0} \dfrac{5^t-3^t}{t}=\ln(5/3)$ 
\item $\lim\limits_{x \to 1} \dfrac{\ln(x)}{x-1}=1$ 
\item $\lim\limits_{x \to \infty} \dfrac{\ln(x)}{\sqrt[3]{x}}=0$
\item $\lim\limits_{t \to 0} \dfrac{\sin(6x)}{\sinh(2x)}=3$ 
\item $\lim\limits_{x \to 0} \dfrac{e^x-1-x-x^2/2}{x^3}=1/6$ 
\item $\lim\limits_{x \to 0} \dfrac{\mathrm{arcsin}(x)}{x}=1$
\item $\lim\limits_{x \to 0} \dfrac{1-e^{2x}}{\sec(x)}=0$
\item $\lim\limits_{x \to 2} \dfrac{\ln(5x-9)}{x^3-8}=5/12$ 
\item $\lim\limits_{x \to 1} \dfrac{\ln(x)}{\tan(\pi x)}=1/\pi$
\item $\lim\limits_{x \to -\infty} x^2e^x=0$
\item $\lim\limits_{x \to 0^+} \sin(x) \ln(x)=0$
\item $\lim\limits_{x \to \infty} x-\ln(x)=\infty$
\item $\lim\limits_{x \to \infty} x^{1/x}=1$
\item $\lim\limits_{x \to 0^+} x^{1/x}=0$
\item $\lim\limits_{x \to 0^+} (\cos(x))^{1/x^2}=1/\sqrt{e}$
\item $\lim\limits_{x \to 0} (1+x)^{1/x}=e$
\item $\lim\limits_{x \to 0^+} x^{\sin(x)}=1$
\item $\lim\limits_{x \to (\pi/2)^-} (\tan(x))^{\cos(x)}=1$
\item $\lim\limits_{x \to \infty} (\ln(x))^{1/x}=1$
\item $\lim\limits_{x \to \infty} (3^x+5^x)^{1/x}=5$
\end{enumerate}
\end{multicols}



\end{document}


\item $\lim\limits_{ \to }$
         \href{}{\ALPHA}

