Sir / Madam
I have adoubt in the folwing section of finding the velocity of a Simple Harmonic Motion (SHM)... I have encircled the place of doubt


I have attached a picture file

my doubt is how to get a w cos wt from d (a sin wt)/dt

where w=omega

Well, that's how the differentiation of trig functions works. I suggest you read up about it.

Differentiation of Trig Functions (http://www.mathsrevision.net/alevel/pages.php?page=10)

thanks for the tip...
but I still don't get it

d (a sinwt)/dt =a coswt but above it states d (a sinwt)/dt =a w coswt

Yes you take the \omega out because that's a constant, whereas you don't take t out because that's the variable of differentiation.