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

Prove that (d)/(dx)("cosec"^(-1)x)=(-1)/(|x|sqrt(x^(2)-1)) , where x in R-[-1,1] .

Prove that (d)/(dx)(sin^(-1)x)=(1)/(sqrt(1-x^(2)) , where x in [-1,1].

Prove that (d)/(dx)(cos^(-1)x)=(-1)/(sqrt(1-x^(2)) , where x in [-1,1].

Prove that (d)/(dx)(cos^(-1)x)=(1)/(sqrt(1-x^(2)) , where x in [-1,1].

Prove that tan(sec^-1 x) = sqrt(x^2 - 1) for x le 1

Prove that tan^(-1) x =sec^(-1) sqrt(1+x^2)

Prove that: d/dx[sin^-1sqrtx]=1/(2sqrt(x-x^2))

If y=tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))] then prove that (dy)/(dx)=(1)/(2sqrt(1-x^(2)))

Prove that tan^(-1).(1)/(sqrt(x^(2) -1)) = (pi)/(2) - sec^(-1) x, x gt 1

Prove that tan^(-1)((1)/(sqrt(x^(2) -1))) = (pi)/(2) - sec^(-1) x, x gt 1