Integral of trigonometric function

1. Jun 19, 2008

Ry122

How do I find the derivative of cos2x?
Do I use the chain rule?
u=2x
u'=2
y=cosu
y'=-sinu
dy/dx=-2sin(2x)
Edit: Sorry. I mean derivative, not integral.

Last edited: Jun 19, 2008
2. Jun 19, 2008

theneedtoknow

That looks good, my friend, so I think you've got it!

3. Jun 19, 2008

rocomath

yes, that's correct

Now try it all in one step!

4. Jun 19, 2008

Ry122

what about the integral of xsin(x/2).
How would I do that?

5. Jun 19, 2008

rocomath

Integral or Derivative? You might want to write it out properly ...

6. Jun 19, 2008

Ry122

integral of xsin(x/2) dx

7. Jun 19, 2008

rocomath

$$\int x\sin{\frac x 2}dx$$

Try integrating by parts.

8. Jun 19, 2008

rootX

use sin(x/2) identity and try to convert everything to sin..

I have a feeling that there's an easier way to do that

9. Jun 20, 2008

tiny-tim

Hi Ry122!

You can also use the chain rule without having to define a u:

dcos2x/dx = (dcos2x/d(2x))(d(2x)/dx) = (-sin2x)(2).

(That way, you can eventually do these things in your head! )