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

If y = tan^(-1)((1+x^(2))/(1-x^(2))) Find dy/dx .

Answer the equation: int tan^(-1)((3x-x^(3))/(1-3x^(2)))dx

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

If y=tan^(-1)((2x)/(1-x^2))" find "(dy)/(dx) .

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)):}

Draw the graph of y=(3x-x^(3))/(1-3x^(2)) and hence the graph of y=tan^(-1).(3x-x^(3))/(1-3x^(2)) .

Prove that tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2)))absxlt(1)/(sqrt(3)).