if `2^x+2^y=2^(x+y)` then the value of `(dy)/(dx)` at `x=y=1`

if y^(x)-x^(y)=1 then the value of (dy)/(dx) at x=1 is

If y=log((1)/(x)) then value of (dy)/(dx) at x=2 is

If x^(y). y^(x)=16 , then the value of (dy)/(dx) at (2, 2) is

Let y=y(x) be the solution of the differential equation (dy)/(dx)=(y+1) ((y+1)e^(x^(2)/2)-x), 0 lt x lt 2.1, with y(2)=0. Then the value of (dy)/(dx) at x=1 is equal to .

If y=1+(x)/(|_(1))+(x^(2))/(|_(2))+......+(x^(n))/(|_(n))+ then the value of (dy)/(dx)-y=

If y=e^((5)/(x))(2x^(2)-1)^((1)/(2)) then the value of ((dy)/(dx))/(y) is

If x^(y) = 2^(x-y) , then (dy)/(dx) =?

if y=(2-x)(3-x)^((1)/(2))(1+x)^(-(1)/(2)) then the value of ([(dy)/(dx)])/(y) is

If sin^(-1)((x^2-y^2)/(x^2+y^2)) = tan^(-1)a, then the value of dy/dx is (i)x/y (ii)-x/y (iii)y/x (iv) -y/x