How do you differentiate # g(x) = 1/sqrtarctan(x^2-1) #?

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Answer 1 · 2018-06-10T04:20:15

#g'(x) = (-x)/(arctan^(3/2)(x^2-1)((x^2-1)^2+1)#

#g(x) = 1/(sqrt((arctan(x^2-1))#

#= [arctan(x^2-1)]^(-1/2)#

#g'(x) -1/2[arctan(x^2-1)]^(-3/2) * d/dx arctan(x^2-1)#

Apply standard derivative and chain rule

#g'(x) -1/2[arctan(x^2-1)]^(-3/2) * 1/(((x^2-1)^2+1)) * d/dx (x^2-1)#

#= -1/2[arctan(x^2-1)]^(-3/2) * 1/(((x^2-1)^2+1)) * 2x#

#= (-x)/[arctan^(3/2)(x^2-1)((x^2-1)^2+1)] #