If #f(x)= cos5 x # and #g(x) = e^(3+4x ) #, how do you differentiate #f(g(x)) # using the chain rule?

1 Answer
Jan 5, 2016

Answer:

Leibniz's notation can come in handy.

Explanation:

#f(x)=cos(5x)#

Let #g(x)=u#. Then the derivative:

#(f(g(x)))'=(f(u))'=(df(u))/dx=(df(u))/(dx)(du)/(du)=(df(u))/(du)(du)/(dx)=#

#=(dcos(5u))/(du)*(d(e^(3+4x)))/(dx)=#

#=-sin(5u)*(d(5u))/(du)*e^(3+4x)(d(3+4x))/(dx)=#

#=-sin(5u)*5*e^(3+4x)*4=#

#=-20sin(5u)*e^(3+4x)#