12,x^(y)+y^(x)=1

Find (dy)/(dx) of the functions given in Exercises 12 to 15. x^(y)+y^(x)=1 .

The centres of the circles x ^(2) + y ^(2) =1, x ^(2) + y^(2)+ 6x - 2y =1 and x ^(2) + y^(2) -12 x + 4y =1 are

Prove that the centres of the circles x^(2)+y^(2)=1,x^(2)+y^(2)+6x-2y-1=0 and x^(2)+y^(2)-12x+4y=1 are collinear

The centres of the circles x ^(2) + y ^(2) =1, x ^(2) + y^(2)+ 6x - 2y =1 and x ^(2) + y^(2) -12 x + 4y =1 are

x^(5).y^(7)=(x+y)^(12)

The circles x^(2)+y^(2)+6x+6y=0 and x^(2)+y^(2)-12x-12y=0

The four lines given by the equations 12 x^(2)+7 x y-12 y^(2)=0 and 12 x^(2)+7 x y-12 y^(2)-x+7 y-1=0 lie along the sides of a

If 2cos alpha = x + (1) / (x), 2cos beta = y + (1) / (y) then (x ^ (10)) / (y ^ (12)) - (y ^ (12)) / ( x ^ (10)) =