How do you differentiate #f(x) = 1/sqrt(arctan(e^x-1) # using the chain rule?

1 Answer
A. S. Adikesavan
Sep 25, 2016

#=-e^x/(2((2-2e^x+e^(2x)) arc tan (e^x-1)sqrt(arc tan (e^x-1)))#

Explanation:

#f'=((arc tan (e^x-1))^(-1/2))'#

#=-1/2(arc tan (e^x-1))^(-3/2)(aec tan(e^x-1))'#

#=-1/2(arc tan (e^x-1))^(-3/2)(1/(1+(e^x-1)^2))((e^x-1)'#

#=-1/2(arc tan (e^x-1))^(-3/2)(1/(1+(e^x-1)^2))(e^x)#

#=-e^x/(2((2-2e^x+e^(2x)) arc tan (e^x-1)sqrt(arc tan (e^x-1)))#

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