If `x sqrt(1-y^2)+y sqrt(1-x^2)=a` then show that `(d^2y)/dx^2=-a/((1-x^2)^(3/2)`

If y=sin^(-1)x , show that (d^2y)/(dx^2)=x/((1-x^2)^(3//2))

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

If sqrt (1-y^2) + sqrt (1-x^2) =a(x-y) , then show that dy/dx = sqrt (frac{1-y^2}{1-x^2})

If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))) , then show that (dy)/(dx) = x/(sqrt(1 - x^4))

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

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

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

If y=sin^(-1)x, show that (d^(2)y)/(dx^(2))=(1)/((1-x^(2))^(3/2))