How do you differentiate # f(x)=(1-xe^(3x))^2# using the chain rule.?

1 Answer
Ratnaker Mehta
Jun 12, 2016

#f'(x) =-2*e^(3x)(1-x*e^(3x))(3x+1).#

Explanation:

#f(x)=(1-x*e^(3x))^2#
#:. f'(x)={(1-x*e^(3x))^2}'#
#=2(1-x*e^(3x)}(1-x*e^(3x)}'#
#=2(1-x*e^(3x)){0-(x*e^(3x))'}#
#=-2(1-x*e^(3x))[x*{e^(3x)}'+e^(3x)(x)']#
#=-2(1-x*e^(3x))[x*(e^(3x))(3x)'#+#(e^(3x))(1)]#
#=-2(1-x*e^(3x))(3x*e^(3x)#+#e^(3x))#
#=-2*e^(3x)(1-x*e^(3x))(3x+1).#

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