#### Answer

Differentiate $y = u(a\cos u + b\cot u)$
$y'=a\cos u + b\cot u -au\sin u -bu\csc ^2u$

#### Work Step by Step

The equation given is $y = u(a\cos u + b\cot u)$.
Use the product rule and the trig rules.
$y' = u'(a\cos u + b\cot u) + u(a\cos u + b\cot u)'$
$=(a\cos u + b\cot u) + u(-a\sin u -b\csc ^2u)$
$=a\cos u + b\cot u -au\sin u -bu\csc ^2u$