y=tan^(-1)((sqrt(x)-4)/(1+x^(3/2)))

If y=tan^(-1)((sqrt(x)-x)/(1+x^((3)/(2)))), then y'(1) is:

Prove that: i) tan^(-1)(sqrt(x)+sqrt(y))/(1-sqrt(xy))=tan^(-1)sqrt(x)+tan^(-1)sqrt(y) ii) tan^(-1)(x+sqrt(x))/(1-x^(3//2))=tan^(-1)x+tan^(-1)sqrt(x) iii) tan^(-1)(sinx)/(1+cosx)=x/2

Solve y=tan^(-1)((sqrt(1+x^(2))-1)/(x))

Solve y=tan^(-1)((sqrt(1+x^2)-1)/x)

Simplify y=tan^(-1)(x/(1+sqrt(1-x^2)))

y=tan^(-1)((x)/(1+sqrt(1-x^(2))))+sin(2tan^(-1)theta*sqrt((1-x)/(1+x))) then prove that ,4(1-x^(2))^(3)((d^(2)y)/(dx^(2)))^(2)+4x=x^(2)+4

y=tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))

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

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)).