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}
$