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How do you find the derivative of #y = cos^3(3x+1)#?

1 Answer

Oct 25, 2016

#(dy)/(dx)=-9sin(3x+1)cos^2(3x+1)#

Explanation:

#y=cos^3(3x+1)#

Applying chain rule: #(dy)/(dx)=(dy)/(du)*(du)/(dx)#

Let #u=cos(3x+1),# then #(du)/(dx)=-3sin(3x+1)#

#(dy)/(du)=d/(du)u^3=3u^2=3cos^2(3x+1)#

#:.(dy)/(dx)=3cos^2(3x+1)*-3sin(3x+1)#

#=-9sin(3x+1)cos^2(3x+1)#

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