## Calculus 8th Edition

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