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 y="tan"^(-1)(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) , then the value of (dy)/(dx) is -

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

If y="cot"^(-1) (sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) , show that [(dy)/(dx)]_(x=(1)/(2))= -(1)/(sqrt(3)) .

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

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

y= tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))) , where -1 < x < 1 , find dy/dx

If tan^(-1)((sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))))=theta , then prove that, sin 2 theta=x^(2) .

If sqrt(1-x^(4))+sqrt(1-y^(4))=k(x^(2)-y^(2)) , prove that, (dy)/(dx)=(xsqrt(1-y^(4)))/(ysqrt(1-x^(4)))

Show that the derivative of (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) w.r.t. sqrt(1-x^(4)) is (sqrt(1-x^(4))-1)/(x^(6)) .

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