If `y=(sqrt(a^2+x^2)+sqrt(a^2-x^2))/(sqrt(a^2+x^2)-sqrt(a^2-x^2))`, show that `(dy)/(dx)=-(2a^2)/(x^3){1+(a^2)/(sqrt(a^4-x^4))}`.

If =(sqrt(a^2+x^2)+sqrt(a^2-x^2))/(sqrt(a^2+x^2)-sqrt(a^2-x^2)) , show that (dy)/(dx)=(2a^2)/(x^3){1+(a^2)/(sqrt(a^4-x^4))} .

If =(sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)+x^(2))-sqrt(a^(2)-x^(2))), show that (dy)/(dx)=(2a^(2))/(x^(3)){1+(a^(2))/(sqrt(a^(4)-x^(4)))}

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 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))) show that, (dy)/(dx)=(x)/(sqrt(1-x^(4)))

If y=sqrt(x)^(sqrt(x)^(sqrt(x)^dotoo)) , show that (dy)/(dx)=(y^2)/(x(2-ylogx)) .

if y=(sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1)), then (dy)/(dx) is

if y=sqrt(x^(2)+a^(2)), then show that y(dy)/(dx)=x

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))

If y=sqrt (a^2-x^2)+a/2 log ((a-sqrt(a^2-x^2))/(a+sqrt(a^2-x^2))) , then find the value of (dy)/(dx)