How do you differentiate # g(x) = 2arcsin(e^(3x)) #?

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Answer 1 · 2017-05-26T17:26:36

#g'(x) = (6e^(3x))/sqrt(1-e^(6x))#

Let #g(x) = y#

#y= 2arcsin(e^(3x))#

#1/2y= arcsin(e^(3x))#

#sin(1/2y) = e^(3x)#

#(1/2cos(1/2y))(dy/dx) = 3e^(3x)#

#dy/dx = (6e^(3x))/cos(1/2y)#

#cos(1/2y) = sqrt(1-sin^2(1/2y)) = sqrt (1-e^(6x))#

#dy/dx = (6e^(3x))/sqrt(1-e^(6x))#