[derivatives of trig functions][section 10]

(1.)   y = sin 3x        here is the problem

y' = 3 cos 3x      use the chain rule

(2.)  y = cos (x - 3)        here is the problem

y' = -sin (x - 3)   use the chain rule

(3.)  y = x cos x              here is the problem

y' = cos x - x sin x   use the product rule

(4.)  y = (sin x)/x              here is the problem

x cos x - sin x
y' =  ___________________  use the quotient rule
x2
______
(5.)  y = √sin x                 here is the problem

y' = (sin x)1/2         use the 1/2 power for radical sign

y' = (1/2)(sin x)-1/2 * cos x     use the chain rule

y' =     cos x
_______________    simplify
______
2√sin x

(6.)   y = (cos x)1/3               here is the problem

y' = (-1/3)(cos x)-2/3 * (sin x)   use the chain rule

- sin x
y' =  _____________          simplify
______
3\3/cos2 x

(7.)  y = sin2 x               here is the problem

y' = 2 sin x cos x            use the chain rule

y' = sin 2x                 simplify (double angle id)

(8.) y = 1 - cos2 x                   here is the problem