Derivative of $f(t)=\frac {1}{\rho}\log (1+\rho t)$ Could you have me to find the ferivative of $$f(t)=\frac {1}{\rho}\log (1+\rho t)$$ with repsect to $t$?
And Is it 
$$\lim_{t\to \infty} \frac {f'(t)}{t}=1?$$
Update:
Based on Hint of Surb:
$$f(t)'=\frac {1}{1+\rho t}$$
Then 
$$\lim_{t\to \infty} \frac {f'(t)}{t}=0$$
Is it correct?

Hint
$$\Big(\log(u(t))\Big)'=\frac{u'(t)}{u(t)}$$
