If f(x) = e^(sin x), how many zeros does f '(x) have on the closed interval [0, 2π]?

Answer 1

f(x)=e^sin(x)
f'(x)=cos(x)e^sin(x)

Where is f'(x)=0?

Answer 2

f'x)=cosx=0
x=pi/2, 3pi/2