If `y=tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]` for `0<|x|<1` ,find `(dy)/(dx)`

If y=tan^(-1)(((sqrt(1+x^(2))-sqrt(1-x^(2)))/((sqrt(1+x^(2))+sqrt(1-x^(2)))) find (dy)/(dx)

y=tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))), where -1

y=(tan^(-1)(sqrt(1+x^(2))+sqrt(1-x^(2))))/(sqrt(1+x^(2))-sqrt(1-x^(2))) then (dy)/(dx)

y=Tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))) then find (8ddy)/(8ddx)

Solve for x:tan^(-1)[(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))]=beta

If tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1-x^(2))+sqrt(1-x^(2)))}=alpha, then prove that x^(2)=sin2 alpha

If tan^(-1). (sqrt((1+x^(2))) - sqrt((1-x^(2))))/(sqrt((1+x^(2)))+sqrt((1-x^(2))))=alpha" , then " x^(2) is