`tan^(- 1){sqrt((a-x)/(2+x))}, -a < x < a`

Differentiate the following functions with respect to x:tan^(-1){sqrt(1+x^(2))-x},x in R (ii) tan^(-1){(sqrt(1+x^(2))-1)/(x)},x!=0

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

Differentiate tan^(-1){sqrt(1+x^(2))+x},x in R with respect to x:

If 0< x< 1 ,then tan^(-1)(sqrt(1-x^2)/(1+x)) is equal to

If 0< x< 1 ,then tan^(-1)(sqrt(1-x^2)/(1+x)) is equal to

Differentiate cos^(-1)(4x^(3)-3x) with respect to tan^(-1)((sqrt(1-x^(2)))/(x)), if 1/2

If x in ((1)/(sqrt(2)), 1) , differentiate tan^(-1) ((sqrt(1-x^2))/(x)) with respect to cos^(-1)(2x sqrt(1-x^2)) .

If x in((1)/(sqrt2)1). Differentiate tan^(-1)(sqrt(1-x^(2))/(x)) w.r. t. cos^(-1)(2xsqrt(1-x^(2))).

If x in((1)/(sqrt2)1). Differentiate tan^(-1)(sqrt(1-x^(2))/(x)) w.r. t. cos^(-1)(2xsqrt(1-x^(2))).