If `y=2 sin^(-1)(x-2)/(sqrt(6))-sqrt(2+4x-x^(2))`, show that, `(dy)/(dx)` at x=2 is `(2)/(sqrt(6))`.

If y = 2 sin^(-1)(x-2)/sqrt6-sqrt(2+4x-x^2) , then show that (dy)/(dx)|_(x=2) = 2/sqrt6

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 = sin^(-1){(5x+12sqrt(1-x^2))/13} then show that (dy)/(dx) = 1/sqrt(1-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)))

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

If x sqrt(1-y^(2))+y sqrt(1-x^(2))=k , then the value of (dy)/(dx) at x=0 is -

If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+log sqrt(1-x^(2)) , show that, (1-x^(2))^(2)(D^(2)y)/(dx^(2))-3x(1-x^(2)))(dy)/(dx)=1

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))) .

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