Weird answer for d(sin(sin(x)))/dx

[ettlz]

Prime 2.0.0.13865 gives a bizarre form of the derivative of sin(sin(x)): I get (1/2)*cos(sin(x)+x) + (1/2)*cos(-sin(x)+x). OK it's correct but I'd expect cos(sin(x))*cos(x) (straightforward chain rule). Getting to that form doesn't work with simplify() and I've not played around with the other trig-rewrite functions.