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Find the derivative of \(\displaystyle f(x)=\sin{\left(x \right)} - 2 \cot{\left(x \right)}\).

Using the sum rule to take the derivative of each term separately gives \(\displaystyle f'(x)=\cos{\left(x \right)} + 2 \cot^{2}{\left(x \right)} + 2\).

Download \(\LaTeX\)

\begin{question}Find the derivative of $f(x)=\sin{\left(x \right)} - 2 \cot{\left(x \right)}$. 
    \soln{9cm}{Using the sum rule to take the derivative of each term separately gives $f'(x)=\cos{\left(x \right)} + 2 \cot^{2}{\left(x \right)} + 2$.}

\end{question}

Download Question and Solution Environment\(\LaTeX\)

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\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}

Find the derivative of <img class="equation_image" title=" \displaystyle f(x)=\sin{\left(x \right)} - 2 \cot{\left(x \right)} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D%5Csin%7B%5Cleft%28x%20%5Cright%29%7D%20-%202%20%5Ccot%7B%5Cleft%28x%20%5Cright%29%7D%20" alt="LaTeX: \displaystyle f(x)=\sin{\left(x \right)} - 2 \cot{\left(x \right)} " data-equation-content=" \displaystyle f(x)=\sin{\left(x \right)} - 2 \cot{\left(x \right)} " /> .

Using the sum rule to take the derivative of each term separately gives <img class="equation_image" title=" \displaystyle f'(x)=\cos{\left(x \right)} + 2 \cot^{2}{\left(x \right)} + 2 " src="/equation_images/%20%5Cdisplaystyle%20f%27%28x%29%3D%5Ccos%7B%5Cleft%28x%20%5Cright%29%7D%20%2B%202%20%5Ccot%5E%7B2%7D%7B%5Cleft%28x%20%5Cright%29%7D%20%2B%202%20" alt="LaTeX: \displaystyle f'(x)=\cos{\left(x \right)} + 2 \cot^{2}{\left(x \right)} + 2 " data-equation-content=" \displaystyle f'(x)=\cos{\left(x \right)} + 2 \cot^{2}{\left(x \right)} + 2 " /> .