How do you differentiate #y= arctan sqrt(x^2 -1) + "arccsc"\ x#?

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How do you differentiate #y= arctan sqrt(x^2 -1) + arccsc x#?

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Answer 1 · 2017-11-15T14:48:32

#y'=0#

#y=arctan(sqrt(x^2-1))+csc^(-1) (x)#

#y'=[(2x)/(2sqrt(x^2-1))]/(x^2-1+1)-1/[x*sqrt(x^2-1)]#

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

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

=#0#