If `y=e^(1+log_(e)x)`, then the value of `(dy)/(dx)` is equal to

If y = x^(1/x) , the value of (dy)/(dx) at x =e is equal to

If y = x^(1/x) , the value of (dy)/(dx) at x =e is equal to

Let y = y (x) be the solution of the differential equation dy = e^(alpha . x + y) dx , alpha in N . If y ( log_(e) 2) = log _(e) 2 and y(0) = log _(e) ((1)/(2)) , then the value of alpha is equal to _____

If y=e^(log_(e)x)," then "(dy)/(dx)=

If y=e^(log_(e)(1+e^(log_(e)x))) then (dy)/(dx)=

if y=log_(2)log_(e)xx then (dy)/(dx) is equal to