`y^(x)=x^(y)`

If x ^(y) + y ^(x) = a ^(b) then show that (dy)/(dx) =- ((y x ^(y-1) + y^(x) log y)/( x ^(y) log x + x y ^(x -1)))

If x=2 and y=4 then x^(y/x)+y^(x/y)= ______

Prove that |(x,y,y),(y,x,y),(y,y,x)| = (x + 2y)(x - y)^(2)

Let f(x,y)=(x-y)/(x+y),x+y!=1, then

If x=2 and y=4 , then ((x)/(y))^(x-y)+((y)/(x))^(y-x) =________.

When simplified (x^(-1)+y^(-1))^(-1) is equal to (a)\ x y (b) x+y (c) (x y)/(x+y) (d) (x+y)/(x y)

The factors of x^3-x^2y-x y^2+y^3 are (a (x+y)(x^2-x y+y^2) (b) (x+y)(x^2+x y+y^2) (c) (x+y)^2(x-y) (d) (x-y)^2(x+y)

x^(y)=y^(x),x=2y

The value of (x-y)^3+(x+y)^3+3(x-y)^2(x+y)+3(x+y)^2(x-y) is

If S=(x+y)(x-y)+(1)/(2!)(x+y)(x-y)(x^(2)+y^(2))+(1)/(3!)(x+y)(x-y)(x^(4)+y^(4)+x^(2)y^(2))+..., then S =