If #f(x)= cos 4 x # and #g(x) = -3x #, how do you differentiate #f(g(x)) # using the chain rule?

2 Answers
May 12, 2016

Answer:

#d/dx(f(g(x))=-12sin12x#

Explanation:

As #f(x)=cos4x# and #g(x)=-3x#, #f(g(x))=cos4(-3x)#

According to chain rule

#d/dxf(g(x))=(df)/(dg)xx(dg)/(dx)#

Hence, as #f(g(x))=cos4(-3x)#

#d/dx(f(g(x))=-4sin4(-3x) xx(-3)#

= #12sin(-12x)=-12sin12x#

May 12, 2016

Answer:

#-12sin(12x)#

Explanation:

#(df)/(dx)=(df)/(dg)(dg)/(dx)#
#=-4sin(4g(x))xx(-3)#
#=12sin(4(-3x))#
#-12sin(12x)#