How do you find the derivative of cos^3(2x)cos3(2x)?

1 Answer
Jim H
Oct 17, 2015

Use the chain rule twice.

Explanation:

First recall that cos^3(2x) = (cos(2x))^3cos3(2x)=(cos(2x))3

So,

d/dx(cos^3(2x)) = 3cos^2(2x) d/dx(cos(2x))ddx(cos3(2x))=3cos2(2x)ddx(cos(2x))

= 3cos^2(2x) (-sin(2x)) d/dx(2x)=3cos2(2x)(−sin(2x))ddx(2x)

= 3cos^2(2x) (-sin(2x)) (2)=3cos2(2x)(−sin(2x))(2)

= -6cos^2(2x) sin(2x)=−6cos2(2x)sin(2x)

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