Question

PLEASE HELP!!!!!!!!!
find the derivative of z=1/2x+1/4 sin2x.

i only got 1/2+1/2 cos2x but my book says the answer is cos^2x... pleaaseee explain it to me.

Answer 1

I think IrishBoy explained you already, right? they are the same.

Answer 2

i still dont get it.. i tried using the double angle but i only get 2cos^2x :/

Answer 3

\(cos (2x) =2cos^2(x) -1\\2cos^2(x) = cos (2x) +1\\cos^2(x) = \dfrac{cos(2x) +1}{2}= \dfrac{1}{2}+\dfrac{cos(2x)}{2}\)

Answer 4

so the only equivalent of cos(2x) is can use is 2cos^2x-1? i cant use the \[\cos2x=\cos^2x-\sin^2x\] ?

Answer 5

Yes, just take one more step : sin^2 = 1 - cos^2
to get cos (2x) = cos^2 - 1+ cos^2 = 2cos^2 -1

Answer 6

it is back to my comment.

Answer 7

\[=1/2(1+\cos^2x-\sin^2x) =1/2(\cos^2x+\cos^2x)=1/2(2\cos^2x)=\cos^2x\] is this fine?

Answer 8

@Loser66 ?

Answer 9

Fine

Answer 10

thanks :) sorry for the trouble.