Let g(x)=cosx. Which of the following correctly describes the sign of g′(x) for all x in the interval (0,π)?
a) g′(x) is positive for all x\;in (0,π)
b) g′(x) changes sign within (0,π)
c) g′(x) is negative for all x\;in (0,π)
d) g′(x) is positive on (0,2π) and negative on (2π,π)