Find the derivative of y = sin2 (4x) cos (3x) with respect to x.

A. 8 sin (4x) cos (4x) cos (3x) - 3 sin2 (4x) sin (3x)

B. 8 sin (4x) cos (3x) - 3 sin2 (4x) sin (3x)

C. 8 sin (4x) cos (4x) cos (3x) - 3 sin2 (4x) sin (3x) cos (3x)

D. 8 cos (4x) cos (3x) - 3 sin2 (4x) sin (3x)

Expanded:

y = sin (4x) * sin (4x) * cos (3x)

need to use the product rule and chain rule

look at individual derivatives, use chain rule

d/dx sin (4x) = 4cos (4x)

d/dx cos (3x) = - 3sin (3x)

put it together using product rule

dy/dx = 4cos (4x) * sin (4x) * cos (3x) + 4cos (4x) * sin (4x) * cos (3x) - 3sin (3x) * sin (4x) * sin (4x)

simplify

dy/dx = 8cos (4x) * sin (4x) * cos (3x) - 3sin (3x) * sin2 (4x)

answer is A.