" (i) "tan^(-1)(sqrt(1+x^(2))+x)

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 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

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

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

Directions (Q. Nos. 16-25) Prove the following "cos"^(-1)x="tan"^(-1)[(sqrt(1-x^(2)))/(x)] .

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

The derivative of tan^(-1) [(sqrt(1 + x^(2)) - 1)/(x)] with respect to tan^(-1) x is

If tan^(-1) (sqrt( 1 +x^(2)) -1)/x = lambda tan^(-1)x then the value of lambda is