Trouble with logarithmic Differentiation

[Duder]

I'm new to logarithmic differentiation and not very confident with the technique. I'm tasked with finding dy/dx given that y = x/(x+lnx)

This is how I approached the problem,

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

dy/dx = y* (1/x -(1+1/x)/(x+lnx)

Then I substituted the y with x/(x+lnx)

Does this look correct? If not, where was my mistake? Thank you

 

[Deleted member 4993]

I'm new to logarithmic differentiation and not very confident with the technique. I'm tasked with finding dy/dx given that y = x/(x+lnx)

This is how I approached the problem,

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

dy/dx = y* (1/x -(1+1/x)/(x+lnx)

Then I substituted the y with x/(x+lnx)

Does this look correct? If not, where was my mistake? Thank you

As far as I can tell you have one unmatched parenthesis. So your answer should look like

dy/dx = y * [1/x - (1 + 1/x)/{x + ln(x)}]