Question

what are the steps to derive (3/4)cos^2(2x)?

Answer 1

the chain's rule again :D

Answer 2

I know, im confused how to use the chain rule with cos^2, though :/

Answer 3

(2x) ' = 2
((cos)^2)'= 2 cos
(cos)' = -sin

then times them

Answer 4

did not know that the derivative of cos^2 was 2cos lol. that is useful

Answer 5

it like derive y^2, get 2y. hehe :)

Answer 6

so, what do you get ?

Answer 7

(3/2)cos2(-sinx)?

Answer 8

2cos*

Answer 9

wait idk lol

Answer 10

(3/2)cosx2(-sinx) maybe?

Answer 11

(3/4)cos^2(2x)
= (3/4) * 2 * 2cos(2x) * (-sin(2x))
= - 3/4 * 4 * sin(2x) cos(2x)

you can cancel the 4's

Answer 12

btw, do you have the answer choices ?

Answer 13

its free response. ok so chain rule is: derivative of the inside * the function * derivative of the function?

Answer 14

yes, inside first. the power, then the function

Answer 15

I have it in my notes as f(g(x)) = f'(g(x))g' does that look right?

Answer 16

correct!

Answer 17

so in my problem f(x) = (cos^2)(x) and g(x) = 2x?

Answer 18

yep

Answer 19

and actually using any identity of trigonometry to simplify it

Answer 20

alright I think I understand this problem, thanks again man :D

Answer 21

it like i want simplify the answer above :
(3/4) * 2 * 2cos(2x) * (-sin(2x))
= - (3/2) * 2cos(2x) * sin(2x)
= -3/2 sin(4x)

you're welcome friend :)