How do you differentiate #f(x)=sin(cos(3x))#?

1 Answer
Nov 18, 2016

#f'(x)= -3sin(3x)cos(cos3x) #

Explanation:

#" "#
#f(x)# is composed of two functions #" "sinx " "and" "cosx#
#f(x)# is differentiated by applying chain rule .
#" "#
Let #u(x) = sinx" " and " "v(x)=cos3x#
#" "#
Then, #" "f(x)=u@v(x)#
#" "#
The differentiation of #f(x)# is :
#" "#
#f'(x)=(u@v(x))'=u'(v(x))xxv'(x)#
#" "#
Computing #u'(v(x))#
#" "#
#u'(x)=cosx#
#" "#
#u'(v(x))=cos(v(x))=cos(cos3x)#
#" "#
#" "#
Computing #v'(x)#
#" "#
#v'(x)=-3sin3x#
#" "#
#" "#
#f'(x)= cos(cos3x)xx (-3sin3x)#

#f'(x)= -3sin(3x)cos(cos3x) #