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

(d)/(dx)[tan^(-1)((4x-4x^(3))/(1-6x^(2)+x^(4)))]=

Tan ^(-1) ((4x - 4x ^(3))/(1 - 6x ^(2) + x ^(4)))

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

Prove that : 1/6tan^(-1)""(2x)/(1-x^2)+1/9tan^(-1)""(3x-x^2)/(1-3x^2)+1/12 tan^(-1)""(4x-4x^3)/((1-6x^2+x^4))= tan^(-1)x

If y=tan^(-1)((4x)/(1-5x^(2)))+tan^(-1)((3+8x)/(8-3x)) , then (dy)/(dx) is :

Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))= tan^(-1)2x,|2x| lt (1)/(sqrt(3)) .

Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))=tan^(-1)2x;|2x|<(1)/(sqrt(3))

If y=tan ^(-1) ((4x)/( 1+5x^(2))) +cot ^(-1) ((3-2x)/( 2+3x)),then (dy)/(dx)=