Question

How do you find the derivative of `csc^-1 (u)`?

Answer 1

`dx/(du)=-1/(usqrt(u^2-1))`

Explanation:

Let `x=csc^-1u`

`u=cscx`

`(du)/dx=-cscxcotx`

`1+cot^2x=csc^2x=u^2`

`cotx=sqrt(u^2-1)`

`(du)/dx=-usqrt(u^2-1)`

`dx/(du)=-1/(usqrt(u^2-1))`