How do you use the chain rule to differentiate #y=cos(3x)#?

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Answer 1 · 2016-10-28T01:10:43

#(dy)/(dx)=-3sin(3x)#

Chain rule is used to differentiate a function within a function:

#(dy)/(dx)=(dy)/(du)*(du)/(dx)#, where #y# and #u# are functions.

#y=cos(3x)#

Let #u=3x, :.y=cos(u)#

#(dy)/(du)=d/(du)cos(u)=-sin(u)=-sin(3x)#

#(du)/(dx)=d/(dx)3x=3#

#:.(dy)/(dx)=-sin(3x)*3=-3sin(3x)#