For f(x)=e^(2sin(x))

Question

find the number of closed zeros for f'(x) on the closed interval [0, 2pi]?

Answer 1

The function

To find , apply derivative on each side with respect of x.

Apply chain rule in derivatives.

on the closed interval [0,2pi]

If

General solution is

For n  = 0

For n  = 1

Closed zeros are .