Question

Find dy/dx if y= (x²-3)³cos2x

Answer 1

dy/dx = 6x(x²-3)cos2x - 2(x²-3)³sin2x

Explanation:

We use the Product Rule:

y= (x²-3)³cos2x

dy/dx = (x²-3)³ d(cos2x)/dx + cos2x * d ((x²-3)³)/dx

= (x²-3)³ * -2sin2x + cos2x * 3(x²-3)*2x

= -2sin2x*(x²-3)³ + 6xcos2x*(x²-3)

= 6x(x²-3)cos2x - 2(x²-3)³sin2x