" 11."(x cos^(-1)x)/(sqrt(1-x^(2)))

If y=(x cos^(-1)x)/(sqrt(1-x^(2)))-log sqrt(1-x^(2)), then prove that (dy)/(dx)=(co^(1-x)x)/((1-x^(2))^((3)/(2)))

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))

Prove that (d)/(dx)(cos^(-1)x)=(1)/(sqrt(1-x^(2)) , where x in [-1,1].

Prove that (d)/(dx)(cos^(-1)x)=(-1)/(sqrt(1-x^(2)) , where x in [-1,1].

The solution set of the equation sin^(-1)sqrt(1-x^(2))+cos^(-1)x=(cot^(-1)(sqrt(1-x^(2))))/(x)-sin^(-1)x is (a) [-1,1]-{0}(b)(0,1)uu{-1}(c)(-1,0)uu{1} (d) [-1,1]

y=sin^(-1)((x)/(sqrt(1+x^(2))))+cos^(-1)((1)/(sqrt(1+x^(2))))

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))))

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)))=