Question #2983a

1 Answer
Feb 16, 2018

#f’(x) = e^sin x cos x (cos^2 x - 3sin x - 1))#

Explanation:

#f(x) = e^sin x (cos^2x - sin x)#

Let’s us apply product rule.

#u = e^sin x, v = (cos^2x - sin x)#

#du = e^sin x cos x#

#dv =( 2 cos x (-sin x) - cos x) = -2 sin x cos x - cos x#

#(d/(dx))(u,v) = u (dv) + v (du)#

#f’(x) =( e^sin x * (-sin (2x) - sin x)) +( (cos^2x - cos x)*(e^sin x cos x))#

#f’(x) = e^sin x (-2sin x cos x - cos x + cos^3x -sin x cos x)#

#f’(x) = e^sinx cos x(cos^2 x - 3sin x - 1)#