Determine y' when?

Question

which of these 3 choices are right....i kinda eliminate the others that i think is not right...but i could be wrong...

A) y(lnx+1)
B) xy (2lnx+1)
C) -y (2lnx-1)

sry y= x^{1/x}

Answer 1

y = x^(1/x)
Take the natural log of each side
ln(y) = ln(x^(1/x))
ln(y) = (1/x)ln(x)
Now take the derivative
y'/y = (-1/x^2)(lnx) + (1/x)(1/x)
y'/y = (1/x^2)(1 - lnx)
Multiply both sides by y.
y' = (y/x^2)(1-lnx)

It doesn't look like any of them are right.

Answer 2

You have not told us what y is, so it's not possible to tell you what y' is.