How do you find the derivative of # arcsin(1/x)#?

1 Answer
Andrew I.
Feb 3, 2016

#-1/(xsqrt(x^2-1))#

Explanation:

#d/dxarcsin(x) = 1/sqrt(1-x^2)#

For #arcsin(1/x)# use the chain rule. Differentiate inside the bracket then multiply that by the derivative for the function surrounding the bracket so:

#d/dx{1/x} = -1/x^2#

#d/dxarcsin(1/x) = -1/x^2 1/sqrt(1-(1/x)^2)#

And now simplify the denominator:

#=-1/x^2 1/sqrt((x^2-1)/x^2) = -1/x^2 x/sqrt(x^2-1) = -1/(xsqrt(x^2-1)) #

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