" (1.) "x sqrt(x+2)

lim _(x to ((1)/(sqrt2))^(+))(cos ^(-1) (2x sqrt(1- x ^(2))))/((x-(1)/(sqrt2)))- lim _(x to ((1)/(sqrt2))^(-))(cos ^(-1) (2x sqrt(1-x ^(2))))/((x- (1)/(sqrt2)))=

(sin ^(-1) x )/( sqrt( 1 - x ^(2)) )

(tan^(-1)x)/(sqrt(1-x^(2))) withrespectto sin ^(-1)(2x sqrt(1-x^(2)))

Evaluate lim_(x rarr 1) (sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1))

lim_(x rarr(1)/(sqrt(2)^(+)))(cos^(-1)(2x sqrt(1-x^(2))))/((x-(1)/(sqrt(2))))-lim_(x rarr(1)/(sqrt(2)^(-)))(cos^(-1)(2x sqrt(1-x^(2))))/((x-(1)/(sqrt(2))))

Differentiate each of the following functions with respect to x:( i) sin^(-1)(2x sqrt(1-x^(2))),-(1)/(sqrt(2))

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