Question

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

Answer 1

`y=sec^-1x^2 rArr dy/dx=2/(|x|sqrt(x^4-1)`.

Explanation:

Let `y=sec^-1x^2`

`:. dy/dx=1/(|x^2|sqrt(x^4-1))*d/dx(x^2)`.

`=(2x)/(|x^2|sqrt(x^4-1))`.

`:. dy/dx=2/(|x|sqrt(x^4-1)`.