Question

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)

Answer 1

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.