" 5."tan(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

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

Find the simplest value of f(x)=tan^(-1)((sqrt(1+x^(2))-1)/(x)),x in R-{0}

The derivative of Tan ^(-1)"" (sqrt(1 + x ^(2))-1)/(x) w.r.t. Tan ^(-1) "" (2x sqrt(1-x ^(2)))/(1 - 2 x ^(2))at x =0 is

Find the derivative of tan^(-1) "" (sqrt(1 + x^(2)) - 1)/( x) with respect to tan^(-1) ( 2 x sqrt( 1 - x^(2)))/(1 - 2 x ^(2)) at x = 0

If tan^(-1)(sqrt(1+x^(2))-1)/x=4^(0) , then

tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

If x lt 0 , then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)))/(x)

If x lt 0 , then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)))/(x)

If x lt 0 , then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)))/(x)