You won't learn unless you figure it out yourself.

Simply (and very briefly) put, make R=0 (a number of terms multiplied by R therefore disappear) BEFORE differentiating, then differentiate and rearrange the equation to group like terms (I think, it's been a while).

Don't forget that when you differentiate sin and cos functions they also change.

http://en.wikipedia.org/wiki/Differentiation_of_trigonometric_functions

http://en.wikipedia.org/wiki/Table_of_derivatives

Thanks but.. I tried 100 times before..

I do not know how equation (3) can be derived from equation (2) by differentiation...

I definitely know what the differentiation is, and how to do it..but this problem is not working with general ways..

I never know what I've been missing..

What seems to be the problem? Are you left with a few extra terms at the end or does your differentiation end in a horrible mess?

Is there a mistake in the supplied equation(s) (it happens all the time, be it homework or not)?

Let's start from the beginning. What is the equation exactly? How was it derived and what is its end result?

Is there another source of this particular equation on the internet (be it homework or for a specific purpose), perhaps without mistakes (if any) or more steps between equation (2) and (3)?

"I do not really understand how equation (2) can be derived from equation (3) by differentiation..."

The note on the JPEG is "derive (3) from (2).

or is this just a typo?

derive (3) from (2) is correct. sorry about this.

The equation -a transfert function I think- is presented in a matrix form.

So that when you want to differentiate you should consider in fact the terms as in the traditional polynomial presentation.

Example: following system can be presented either as 2 equations or in a matrix form (as equation (2) in your presentation))

a1*x+b1*y=c1

a2*x+b2*y=c2

If you differentiate the 1st equation you obtain:

a1'*x+a1*x'+b1'*x+b1*x' = c1'

which you can group after again in a matrix form.

The best for you is to go from the matrix form to the polynomial presentation, make the derivation considering that all variables are time dependent and then go back to the matrix form.

This way you will better understand why some terms in equation (3) only seem to have no reason to be. I presume this was you problem.

Hope it will help.