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

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Answer 1 · 2016-08-05T14:34:21

$d/(dx)sec^(-1)(x^2-x)=(2x-1)/(|x^2-x|sqrt((x^2-x)^2-1))$

As derivative of $sec^(-1)x=1/(|x|sqrt(x^2-1))$ , using chain rule,

$d/(dx)sec^(-1)(x^2-x)=1/(|x^2-x|sqrt((x^2-x)^2-1))xx(2x-1)$

= $(2x-1)/(|x^2-x|sqrt((x^2-x)^2-1))$

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