Lets see if I learned from the last one.
Should be product rule again on left-hand side, and I'm not at all sure what you're aiming at there on the right (should be chain rule). Balloons approaching...
Edit:
I see now that you were trying for the product rule but forgot the plus sign. Anyway...
Just in case it helps to see the formulae as well...
and
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You still want to see a dy/dx on the right hand side? Not so...
LHS good.
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Don't integrate - balloontegrate!
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Yes but don't put it in if it doesn't belong... are you confusing dy/dx with d/dx? It's leading you down a wrong turn - your next line is way off
Edit:
Your factorising and so on are fine - subject the bottom row of my pic to the same processes and you should arrive at the correct derivative. Then have a think about why you were taking a different turn... probably the d/dx notation, which actually just means 'derivative (with respect to x) of...' (You don't need it anyway if you draw the picture!)
just means the derivative of sin(2x).
The chain rule says that the derivative of sin(anything) is cos(the same thing) times the derivative of the thing...
Try to read d/dx as just saying 'the derivative of' - or use a picture and do without it, because d/dx of anything is whatever's in the balloon below...