If `x^y=y^x,` then `(x/y)^(x//y)` is equal to a. `x^(y//x)` b. `x^(x/y-1)` c. `1` d. `x^(x/y)`

If x^(y)=y^(x), then ((x)/(y))^(x/y) is equal to a.x^(y/x) b.x^((x)/(y)-1) c.1d.x^((x)/(y))

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

If y=cos^(-1)(cosx),t h e n(dy)/(dx) is equal to x/y (b) y/(x^2) (x^2-y^2)/(x^2+y^2) (d) y/x

If x=e^(y+e^(y+e^y^(------ ∞))) , x>0 , then (dy)/(dx) is equal to (A) (x)/(1+x) (B) (1)/(x) (C) (1-x)/(x) (D) (1+x)/(x)

If f(x)=cos((log)_e x),\ t h e n\ f(1/x)f(1/y)-1/2{f(x y)+f(x/y)} is equal to a. "cos"(x-y) b. log(cos(x-y)) c. 0 d. "cos"(x+y)

If a=(x)/(x+y) and b=(y)/(x-y), then (ab)/(a+b) is equal to (a) (xy)/(x^(2)+y^(2)) (b) (x^(2)+y^(2))/(xy)( c) (x)/(x+y) (d) ((y)/(x+y))^(2)

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

If y=(sin^(-1)x)^2,\ then (1-x^2)y_2 is equal to x y_1+2 (b) x y_1-2 (c) x y_1+2 (d) none of these