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How do you differentiate #g(x) = xsqrt(1-e^(2x))# using the product rule?

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Jun 18, 2018

Answer:

#g'(x)=sqrt(1-e^(2x))-(x*e^(2x))/(sqrt(1-e^(2x))#

Explanation:

After the product and the chain rule we get

#g'(x)=sqrt(1-e^(2x))+x+1/2*(1-e^(2x))^(-1/2)*(-e^(2x))*2#
this simplifies to

#g'(x)=sqrt(1-e^(2x))-(x*e^(2x))/sqrt(1-e^(2x))#

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