How do you find the derivative of #f(x)=(2-4e^(2x))^3 #?

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Answer 1 · 2017-11-21T21:01:50

#-24(2-4e^(2x))^2*e^(2x)#

This problem is best solved by a double application of the chain rule

#d/dx((2-4e^(2x))^3)=#

Let #u=2-4e^(2x)#:

#=d/(du)(u^3)d/dx(2-4e^(2x))=#

Let #z=2x#:

#=3u^2*d/(dz)(2-4e^z)d/dx(2x)=#

#=3u^2*-4e^z*2=-24u^2*e^z=#

Resubstitute:

#=-24(2-4e^(2x))^2*e^(2x)#