" 8."y=tan^(-1)(3a^(2)x-x^(3))/(a(a^(2)-3x^(2)))

if y=(tan^(-1)(3a^(2)x-x^(3)))/(a(a^(2)-3x^(2))) then (dy)/(dx)

y=tan^(-1)((3a^2x-x^3)/(a(a^2-3x^2)))

If tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))=k tan^(-1)(x/a) then k=

Prove that tan^(-1)""(3a^(2)x-x^(3))/(a^(3)-3ax^(2))=3tan^(-1)""x/a .

If y = tan^(-1)((3x-x^(3))/(1-3x^(2))) + tan^(-1) ((4x-4x^(3))/(1-6x^(2) + 4x^(4))) then (dy)/(dx) =

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

Prove that tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1

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: i) sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2 ii) cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1 iii) tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3) iv) tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))