`tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2))),a gto,(-a)/(sqrt(3))lt x lt (a)/(sqrt(3))`

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

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)):}

Differentiate tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)),\ -1/(sqrt(3))

Differentiate tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)),\ -1/(sqrt(3))

y=tan^(-1)""(3x-x^(3))/(2x^(2)-1),-(1)/(sqrt(3))ltxlt(1)/(sqrt(3))

If y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(sqrt(3))ltxlt1 /(sqrt(3)), then find (dy)/(dx)

tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lt a

Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , |x|<1/sqrt3 w.r.t tan^(-1)(x/sqrt(1-x^2))