x^(y)y^(x)=1

If x^(y)=y^(x) show that (x/y)^(x/y)=x^((x)/(y)-1) if further x=2y then prove that y=2

If x^y=y^x , then prove that (x/y)^(x/y)=(x)^((x)/(y)-1) .

Find the area bounded by (x-y)(x+y)=1 and x^2+y^2=4, x gt 0, y gt 0 .

Find the area bounded by (x-y)(x+y)=1 and x^2+y^2=4, x gt 0, y gt 0 .

If x^y+y^x= (x+y)^(x+y) , then prove that dy/dx= ((x+y)^(x+y) [1+log(x+y)]-yx^(y-1)-y^xlogy)/(x^ylogx+xy^(x-1) -(x+y)^(x+y) [1+log(x+y)]

Find the sum of G.P. : (x+y)/(x-y)+1+(x-y)/(x+y)+ . . . . .. . . . upto n terms.

Find the sum of the following series (x+y)/(x-y)+1+(x-y)/(x+y)+ …. to n th term.

(x/y)^(-1)=(x)^(-1)/(y)^(-1)