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Question

#d/(dx)(ln(e^x((x-1)/(x+1))^(3/2))=?#

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Answer 1 · 2017-12-05T11:52:33

# (x^2+2)/(x^2-1)#

First

#log(e^x((x-1)/(x+1))^(3/2)) = x+3/2(log(x-1)-log(x+1))# and then

#d/(dx)log(e^x((x-1)/(x+1))^(3/2)) = 1+3/2(1/(x-1)-1/(x+1)) = 1+3/(x^2-1) = (x^2+2)/(x^2-1)#