Differentiate if
`y=cos^(-1)frac (sqrt x-1)(sqrt x+ 1)+cosec^(-1)frac (sqrt x+1)(sqrt x- 1)`

Differentiate tan^(-1) frac x(1+sqrt(1-x^2))

Differentiate (x sin^(-1) x)/(sqrt (1 + x^2))

Differentiate cos^(-1)sqrt((1+cos x)/(2)) w.r.t. x.

Differentiate tan^(-1) frac cos x( 1+ sin x)

Show the dy/dx is independent of t if. x = cos^(-1) frac 1(sqrt(t^2 + 1)) and y = sin^(-1) frac t(sqrt(t^2 +1))

If y=x^2cos^(-1)(frac[sqrtx-1][sqrtx+1])+x^2cosec^(-1)(frac[sqrtx+1][sqrtx-1]) then prove that frac[d^2y][dx^2]=pi

Differentiate tan^(-1) frac((cos x-sin x))((cos x+ sin x))

Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) w.r.t x .

Differentiate tan^(-1) frac (7x)(1-12x^2)

Differentiate tan^(-1) frac (sqrt(1+x^2) + sqrt(1-x^2))(sqrt(1+x^2) - sqrt(1-x^2))