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

1 Answer
Oct 17, 2016

d/(dx)cos^2(3x)=-6sin(3x)cos(3x)

Explanation:

Using the chain rule, we can treat cos(3x) as a variable and differentiate cos^2(3x) in relation to cos(3x).

Chain rule: (dy)/(dx)=(dy)/(du)*(du)/(dx)

Let u=cos(3x), then (du)/(dx)=-3sin(3x)

(dy)/(du)=d/(du)u^2->since cos^2(3x)=(cos(3x))^2=u^2

=2u=2cos(3x)

(dy)/(dx)=2cos(3x)*-3sin(3x)=-6sin(3x)cos(3x)