How do you differentiate # (e^(2x) + 2x) ^0.5#?

1 Answer
Jim G.
Jan 13, 2016

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

Explanation:

#f(x) = (e^(2x )+ 2x )^(1/2)#

using the chain rule :(twice)

#f'(x) = 1/2(e^(2x) + 2x )^(-1/2) . d/dx (e^(2x) + 2x )#

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

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

#= 1/2 (e^(2x) +2x )^(-1/2) .2 ( e^(2x) + 1 ) #

#rArrf'(x) = (e^(2x) + 1 )/(e^(2x) + 2x )^(1/2) #

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