## En one year ago 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.

1. Loser66

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

2. En

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

3. Loser66

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

4. En

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

5. Loser66

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

6. Loser66

it is back to my comment.

7. En

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

8. En

@Loser66 ?

9. Loser66

Fine

10. En

thanks :) sorry for the trouble.