Question

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

Answer 1

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

Explanation:

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))`