Find the derivative of $LaTeX: \displaystyle f(x)=- \cos{\left(x \right)} - 8 \cot{\left(x \right)}$ .

Using the sum rule to take the derivative of each term separately gives $LaTeX: \displaystyle f'(x)=\sin{\left(x \right)} + 8 \cot^{2}{\left(x \right)} + 8$ .