If `tan^(-1)(sqrt(1+x^2-1))/x=4^0` then `x=tan2^0` (b) `x=tan4^0` `x=tan1/4^0` (d) `x=tan8^0`

Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)x ,x!=0.

Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)x ,x!=0.

Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)x , when x!=0.

Differentiate tan^-1((4sqrt(x))/(1-4x))

The solution of the differential equation (1+x^2)(dy)/(dx)+1+y^2=0, is a) tan^(-1)x-tan^(-1)y=tan^(-1)C b) tan^(-1)y-tan^(-1)x=tan^(-1)C c) tan^(-1)y+-tan^(-1)x=tan^(\ )C d) tan^(-1)y+tan^(-1)x=tan^(-1)C

Differentiate tan^(-1)'(sqrt(1+x^(2))-1)/(x) w.r.t. tan^(-1)x , when x ne 0 .

Write each of the following in the simplest form: tan^(-1){(sqrt(1+x^2)+1)/x},\ \ x!=0 (ii) tan^(-1) { sqrt((a-x)/(a+x)) } ,\ \ -a

The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)((2xsqrt(1-x^2))/(1-2x^2)) at x=0 is 1/8 (b) 1/4 (c) 1/2 (d) 1

The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)((2xsqrt(1-x^2))/(1-2x^2)) at x=0 is 1/8 (b) 1/4 (c) 1/2 (d) 1

Let |[tan^(-1)x,tan^(-1)2x,tan^(-1)3x],[tan^(-1)3x,tan^(-1)x,tan^(-1)2x],[tan^(-1)2x,tan^(-1)3x,tan^(-1)x]| =0 , then the number of values of x satisfying the equation is (a) 1 (b) 2 (c) 3 (d) 4