"tan^(-1)"((sqrt(x)-x)/(1+sqrt(x^(3))))"

If f(x)=tan^(-1)((sqrt(3)x-3x)/(3sqrt(3)+x^(2)))+tan^(-1)(x/(sqrt(3))),0lexle3, then range of f(x) is

tan^(-1)((sqrt(x))/(1+20x))

tan^(-1)((sqrt(x)(3-x))/(1-3x))

Prove that tan^(-1) ((1-sqrt(x))/(1+sqrt(x))) = pi/4 - tan^(-1) sqrt(x) , "where" x gt 0

tan^(-1)(sqrt((1-x)/(1+x)))

tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

tan^(-1)((x)/(sqrt(1-x)))

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

If y=tan^(-1){(sqrt(1+x^(3))-sqrt(1-x^(3)))/(sqrt(1+x^(3))+sqrt(1-x^(3)))} , then (dy)/(dx)=(kx^(2))/(sqrt(1-x^(6))) ,where k is equal to