ummm almost done but how do i differentiate piecewise functions ? I've done the graphing on paper and i dont know how to graph it on the site to show you but the least i can say is i've graphed the piecewise function but now i need to differentiate it. I've differentiated the little pieces in the piecewise function but the intervals somehow change when i differentiate it. I don't understand that. What i mean is when something in a piecewise function is

x+6 x >=3 which is normal part inside piecewise function then when i differentiate it the interval becomes:

x+6 x > 3 what happened to the x being greater or equal to 3 after i differentiated it ? how does that vanish after differentiating that little part in the entire piecewise function and if u dont know what function im talking about look at my first post on this threat and that x+6 x>3 i got from my answer sheet but i dont know why or how it changes