# 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.

Last edited:
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#### 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

Homework Helper
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! )

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