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)#