" If "sqrt(x)+sqrt(x-sqrt(1-x))=1," then show that "x=(16)/(25)

If sqrt(x)+sqrt(x-sqrt(1-x))=1 then value of x is

sqrt(x+1)-sqrt(x-1)=sqrt(4x-1)

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

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

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

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

If x - sqrt((sqrt5+1)/(sqrt5-1)) , show that x^2-x-1=0

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 e^(y)=(sqrt(1+x)+sqrt(1-x))/(sqrt(1+x)-sqrt(1-x))," then "(dy)/(dx)=