Single Variable Calculus, Chapter 3, 3.4, Section 3.4, Problem 8

Differentiate $\displaystyle y = u(a \cos u + b \cot u)$


$\begin{equation} \begin{aligned} y' =& au \cos u + bu \cot u && \\ \\ y' =& au \frac{d}{du} (\cos u) + \cos u \frac{d}{du} (au) + bu \frac{d}{du} (\cot u) + \cot u \frac{d}{du} (bu) && \text{Derive each term} \\ \\ y' =& (au) (-\sin u) + (\cos u) (a) + (bu)(-\csc^2 u) + (\cot u) (b) && \text{Simplify the equation} \\ \\ y' =& a \cos u + b \cot u - au \sin u - bu \csc^2 u && \text{} \end{aligned} \end{equation}$