Question

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

Answer 1

cos(x) * e^(sin(x)) = 0 when x = pi/2 and 3pi/2

Answer 2

e^(sin[x])*cos[x]=0 and solve for x
it is zero when cos[x] is zero namely; at pi/2, 3pi/2 in [0,2pi]

Answer 3

How'd you guys get cos(x)??

Answer 4

its the chain rule of derivatives

Answer 5

Du e^u; u = sin(x)

cos(x) e^(sin(x))

Answer 6

got it! Thanks :)