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

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

Write the following in the simplest form: tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))

Differentiate the following functions with respect to x:tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))

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

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

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

For any a,b,c,x,y>0 prove that :(2)/(3)tan^(-1)((3ab^(2)-a^(3))/(b^(3)-3a^(2)b))+(2)/(3)tan^(-1)((3xy^(2)-x^(3))/(y^(3)-3x^(2)y))=tan^(-1)(2 alpha beta)/(a^(2)-beta^(2)) where alpha=-ax+by,beta=bx+ay

Sketch the graph for y=tan^(-1)((3x-x^(3))/(1-3x^(2)))