If `y=(xsin^(-1)x)/(sqrt(1-x^2))+logsqrt(1-x^2)` , then prove that `(dy)/(dx)=(sin^(-1)x)/((1-x^2)^(3/2))`

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

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

If y = (x sin^(-1) x)/(sqrt(1 - x^2)) + "log" sqrt(1 - x^2) , prove that (dy)/(dx) = (sin^(-1)x)/((1 - x^2)^(3//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)))

If y=x\ sin^(-1)x+sqrt(1-x^2) , prove that (dy)/(dx)=sin^(-1)x

If y=x sin^(-1)x+sqrt(1-x^(2)), prove that (dy)/(dx)=sin^(-1)x

If y=x sin^(-1)x+sqrt(1-x^(2)), prove that (dy)/(dx)=sin^(-1)x

If y= sin^(-1)(x/(sqrt(1+x^2))) + cos^(-1)(1/(sqrt(1+x^2))) , prove that (dy)/(dx)=(2x)/(1+x^2) .

If x sqrt(1+y)+y sqrt(1+x)=0, then prove that (dy)/(dx)=-(1+x)^(-2)

If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))