Vector calculus on particle movement

Hello,

I'm currently working on a question which is about a particle moving across along a line. The particle is moving along the line log (x) at a constant speed of one. When t = 0, the particle is at point (1,0). I have to find a) the velocity vector and b) the acceleration vector at (1,0).

I've start off by making $\displaystyle r(t) = (x(t), \log (x(t))$. To find the velocity vector, I must differentiate $\displaystyle r(t)$. So: $\displaystyle v(t) = r'(t) = (x'(t), \frac{x'(t)}{x(t)})$. This is where I get stuck. I know that the speed of the particle is 1 at any time t. So $\displaystyle \mid v(t)\mid = x'(t)\sqrt{1+\frac{1}{(x(t))^2}}=1$. I feel I need to find the value x'(t). Is this right? If so, how do I find it?

Thanks for your help.