If `x-sqrt(a^(2)-y^(2))=a" log"(a-sqrt(a^(2)-y^(2)))/(y)`, show that,
`(dy)/(dx)=(y)/(sqrt(a^(2)-y^(2)))`

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

(dy)/(dx)=sqrt(4-y^(2))

If xy=a[y+sqrt(y^(2)-x^(2))] , prove that, x^(3)(dy)/(dx)=y^(2)(y+sqrt(y^(2)-x^(2)))

If y="tan"^(-1) (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) 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)))/(sqrt(1-x^(2))) .

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

If x=sqrt(a^(sin^(-1)t)), y= sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)= -(y)/(x) .

If x=sqrt(a^(sin^(-1)t)" and "y=sqrt(a^(cos^(-1)t) show that (dy)/(dx)=-(y)/(x) .

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