well actually i have two quick questions. i am doing a problem and i wanted to make sure my thought process was correct.

1. when you have an integral, lets say inside the integral is 3*e^((1/2)*sin (2t)dt) with the limits running from 0 to x, if I wanted to take the derivative of this integral then that would simply remove the integral and leave me with the function at the endpoints of 0, and x? so i would have 3*e^((1/2)*sin (2(x)) dt - 3*e^((1/2)*sin (2(0)) dt ? is this correct?

2. my second question is on taking the derivative of the function y= e^(-(1/2)*sin(2x)). to do this derivative i could say -2*(1/2)*cos(2x)?

thanks in advance