" 9."(dy)/(dx)=(y)/(x)(log(y)/(x)+1)

The differential equation representing the family of curves y=xe^(cx) (c is a constant ) is a) (dy)/(dx)=(y)/(x)(1-"log"(y)/(x)) b) (dy)/(dx)=(y)/(x)"log"((y)/(x))+1 c) (dy)/(dx)=(y)/(x)(1+"log"(y)/(x)) d) (dy)/(dx)+1=(y)/(x)"log"((y)/(x))

If x^(y)=y^(x) , prove that (dy)/(dx)=((y)/(x)-log y)/((x)/(y)-log x)

(dy)/(dx)=(x+y)ln(x+y)-1

If y=x^(x^(x^(...oo))) , then prove that, (dy)/(dx)=(y^(2))/(x(1-y log x)) .

If y = x^y , prove that (dy)/(dx) = (y^2)/(x(1 - y log x))

If x^(y)y^(x),=1, prove that (dy)/(dx),=-(y(y+x log y))/(x(y log x+x))

If x^(y).y^(x)=1, prove that (dy)/(dx)=-(y(y+x log y))/(x(y log x+x))

If y=a^(x^(x^(2)*oo)), prove that (dy)/(dx)=(y^(2)log y)/(x(1-y log x*log y))

If x ^( log y) = log x, then prove that (dy)/(dx) = (y)/(x) ((1- log x log y)/( (log x) ^(2)))

"If "x^(y)=e^(x-y)," prove that "(dy)/(dx)=(log x)/((1+log x)^(2)).