3) Find the first partial derivatives of the function f(x, y) Y) sin (et) dt = 2X

I thought the derivative of sin(e^2x) was 2e^2xcos(e^2x) but in the answer we just have sin(e^2x)(2x)d/dx. Is that correct? 

After seeing the additional solution for Fx(x,y), shouldn't it be -2sin(e^2x) instead of positive 2sin(e^2x) since it is Fx = 0 - sin(e^2x)(2)

Do I not have to do anything to find the other partial derivative Fx? Or is that just 0? Also does that second part become 0 becuase the d/dy means we take the derivative in respect to y and there are none (only sin(e^2x) and 2x) so it is 0? Sorry for the questions it has been a very long time since I've done any math so I'm struggling a bit to grasp the concepts on this problem. Thanks!