How do you differentiate f(x)=(1-xe^(3x))^2f(x)=(1−xe3x)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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