Hmmm...

I'm having a bit of trouble using the chain rule. I thought that I was applying it correctly, but I keep obtaining the wrong answer. :bugeye: Oh yeah, this involves natural log's.

y= logex+loge(x+1)

y=loge[x(x+1)]

y= loge[x^2+x)

Let u = x^2+x

du/dx= 2x+1

Let y = logeu

dy/du = 1/u

dy/dx = dy/du * du/dx

= 1/u * 2x + 1

=(2x+1)/u

=(2x+1)/(x^2+x)

WRONG ANSWER!
And this isn't the only question I'm getting wrong. However, if I work out what I done wrong here, then I guess the same rule applies.

Is the correct answer given as 1/x + 1/(x+1)?

That's the same thing as your answer.
The difference is in your first step - don't combine the two logs, differentiate them individually:

y = u + v
dy/dx = du/dx + dv/dx