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

$y'=0$

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

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

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

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

= $0$