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

1 Answer
Oct 28, 2016

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

Explanation:

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)