tan^(-1)((3-2x)/(1+6x))

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)).

(d)/(dx)[tan^(-1)((6x)/(1+7x^(2)))]+(d)/(dx)[tan^(-1)((5+2x)/(2-5x))]=

If y = tan^(-1) (x/(1 + 6x^2)) + tan^(-1) ((2x - 1)/(2x + 1)), (AA x > 0) then (dy)/(dx) is equal to

If y = tan^(-1) (x/(1 + 6x^2)) + tan^(-1) ((2x - 1)/(2x + 1)), (AA x > 0) then (dy)/(dx) is equal to

Given that , tan^(-1) ((2x)/(1-x^(2))) = {{:(2 tan^(-1) x"," |x| le 1),(-pi +2 tan^(-1)x","x gt 1),(pi+2 tan^(-1)x"," x lt -1):} sin^(-1)((2x)/(1+x^(2))) ={{:(2 tan^(-1)x","|x|le1),(pi -2 tan^(-1)x","x gt 1 and ),(-(pi+2tan^(-1))","x lt -1):} sin^(-1) x + cos^(-1) x = pi//2 " for " - 1 le x le 1 If cos^(-1). (6x)/(1 + 9x^(2)) = - pi/2 + 2 tan^(-1) 3x" , then " x in

f(x)=tan^(-1){(log((e)/(x^(2))))/(log(ex^(2)))}+tan^(-1)((3+2log x)/(1-6log x)) then find (d^(n)y)/(dx^(n))

If the function f:R rarrA defined as f(x)=tan^(-1)((2x^(3))/(1+x^(6))) is a surjective function, then the set A is equal to

If the function f:R rarrA defined as f(x)=tan^(-1)((2x^(3))/(1+x^(6))) is a surjective function, then the set A is equal to

If y=tan^(-1)((log((e)/(x^(2))))/(log(ex^(2))))+tan^(-1)((3+2log x)/(1-6log x)) then (d^(2)y)/(dx^(2)) is (a) 2(b)1(c)0(d)-1

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