[n=tan^(-1)(sqrt(x^(2)-2x+2))],[n=rho_(0)t^(-1)__|_(0)-x^(2)-2x^(2)]

tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))],|x|<(1)/(2),x!=0

Differentiate tan^(-1)((sqrt(1+x^(2))+1)/(x))" w.r.t. "tan^(-1)((2xsqrt(1-x^(2)))/(1-2x^(2))) at x = 0.

The value of tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))]=theta, |x|<1/2,x!=0 , is equal to:

Derivative of tan ^(-1) ((sqrt( 1+x^(2))-1)/( x)) w.r.t. tan ^(-1) ((2x sqrt(1-x^(2)))/( 1-2x ^(2))) is

If y = tan^(-1) ((1)/(1 + x + x^(2))) + tan^(-1) ((1) /(x^(2) + 2x + 3)) + tan^(-1) ((1)/(x^(2) + 5x + 7)) + ….n terms , then y(0) is