Let f(t) be a differential curve such that $f(t)\not=0$. Now, how to show that $$\frac{d}{dt}(\frac{f(t)}{||f(t)||}=\frac{f(t)\times (f'(t)\times f(t))}{||f(t)||^3}\tag{1}$$
My attempt: $$\frac{d}{dt}\left(\frac{f(t)}{||f(t)||}\right)=\frac{d}{dt}\left(\frac{1}{||f(t||}\right)*f(t)+\frac{1}{||f(t)||}*\frac{d}{dt}(f(t))$$
$$=-\frac{(||f(t||')*f(t)}{||f(t)||^2}+\frac{f'(t)}{||f(t)||}$$
Now where to go from here to get R.H.S of (1)?