[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

     y' = sin 2x     [use your answer from number (7.) above]

(9.)  y = 2 sin x cos x         here is the problem

      y = sin 2x         (double angle identity)

     y' = 2 cos 2x     use the chain rule

(10.)   y = sin2 x - cos2 x     here is the problem

       y = - cos 2x           (double angle id for cos)

       y' = 2 sin 2x      use the chain rule