Find `(dy)/(dx)` in the following :
`y = tan^(-1)((3x-x^(3))/(1-3x^(2))), -(1)/(sqrt(3)) lt x lt (1)/(sqrt(3))`.

Find (dy)/(dx) in the following : y= sin^(-1) (2x sqrt(1-x^(2))), (1)/(sqrt(2)) lt x lt (1)/(sqrt(2)) .

y = tan^(-1)((3x-x^(3))/(1-3x^(2))), find dy/dx.

Find (dy)/(dx) in the following : y= sin^(1)((1-x^(2))/(1+x^(2))), 0 lt x lt 1 .

Find (dy)/(dx) in the following : y= cos^(-1) ((1-x^(2))/(1+x^(2))), 0 lt x lt 1 .

Find (dy)/(dx) in the following : y= cos^(-1) ((2x)/(1+x^(2))), -1 lt x lt1 .

Find (dy)/(dx) in the following : y= sec^(-1) ((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt(2)) .

Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}

Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

Find the range of f(X) = tan^(-1)x-(1)/(2)log_(e)x in (1)/(sqrt(3)),(sqrt(3))