If `x^(y)=e^(x-y)," then "(1+logx)^(2)y_(1)=`

If x^(y)=e^(x)," then "(logx)^(2)y_(1)=

If e^(x)+e^(y)=e^(x+y)" then "y_(1)=

If x^y=e^(x-y) , then (dy)/(dx) is (a) (1+x)/(1+logx) (b) (1-logx)/(1+logx) (c) not defined (d) (logx)/((1+logx)^2)

If y=tan^(-1)((2)/(e^(-x)-e^(x)))" then "(1+e^(2x))y_(1)=

If x^(y)=e^(x-y) then prove that (dy)/(dx)=(logx)/((1+logx)^(2))

If y=log(logx)," then "xy_(2)+x(y_(1))^(2)=

If e^(y) (x+1) =1,then y_2=

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