Simple explanation of the differentiation of $\ln(f(x))$ Could somebody explain why the derivative of $\ln[f(x)]$ = $f'(x)/f(x)$ .
Why is it not simply $1/f(x)$ as is the case for the derivative of $\ln(x)$ being $1/x$? 

what we wish to find is 
$$\lim_{\Delta x\to 0} \frac{\ln f(x+\Delta x)-\ln f(x)}{\Delta x}$$
This can be found easily by using the chain rule (e.g. $\frac{\Delta y}{\Delta x} = \frac{\Delta y}{\Delta u}\cdot\frac{\Delta u}{\Delta x}$).
What $1/f(x)$ represents is
$$\lim_{\Delta f(x)\to 0} \frac{\ln (f(x)+\Delta f(x))-\ln f(x)}{\Delta f(x)}$$
