What is the derivative of this function #y=sec^-1(x^2)#?

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Answer 1 · 2017-10-24T11:55:31

#dy/dx= 2/(xsqrt(x^4-1)#

#y = sec^-1 (x^2)#

#y = arccos(1/x^2)#

Apply standard differential and chain rule

#dy/dx= (-1/sqrt(1-(1/x^2)^2)) * d/dx (1/x^2)#

#dy/dx = -1/sqrt(1-1/x^4) * -2/x^3#

#= 1/sqrt(x^4-1) * sqrt(x^4) * 2/x^3#

#= 1/sqrt(x^4-1) * x^2 * 2/x^3#

#= 2/(xsqrt(x^4-1)#