Integral of trigonometric function

[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.

 

[theneedtoknow]

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

 

[rocomath]

yes, that's correct

Now try it all in one step!

 

[Ry122]

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

 

[rocomath]

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

 

[Ry122]

integral of xsin(x/2) dx

 

[rocomath]

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

Try integrating by parts.

 

[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

 

[tiny-tim]

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.

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! )