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#### Dhamnekar Winod

##### Active member

- Nov 17, 2018

- 103

Let f(t) be a differentiable curve such that $f(t)\not= 0$ for all t. How to show that $\frac{d}{dt}\left(\frac{f(t)}{||f(t)||}\right)=\frac{f(t)\times(f'(t)\times f(t))}{||f(t)||^3}\tag{1}$

My attempt:

$\frac{d}{dt}\left(\frac{1}{||f(t)||}\right)*f(t)+\frac{1}{||f(t)||}*\frac{d}{dt}(f(t))$

$\frac{||f(t)||}{f'(t)\cdot f(t)}*f(t) +\frac{1}{||f(t)||}*\frac{d}{dt}(f(t))$

I want to know whether my last step is correct or wrong.If wrong , how and where to go from here to get

**R.H.S.of (1)**? If yes how to proceed further to get

**R.H.S.of (1)?**