[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