- #1
WMDhamnekar
MHB
- 378
- 28
Hi,
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)?
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)?