[微積] a problem about vector-value function

看板Math作者 (真是太酷了)時間13年前 (2012/04/24 21:10), 編輯推噓2(2推 0噓 7→)
留言9則, 3人參與, 最新討論串1/1
Let f be a differentiable vector-valued function. Compute d/dt(f(t)/||f(t)||)=? Please help me resolve this problem, Thanks a lot -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.228.68.120
推
04/24 21:18, , 1F
just write f in vector form
04/24 21:18, 1F
→
04/24 21:22, , 2F
||f(t)|| = √f(t)．f(t) ?
04/24 21:22, 2F
→
04/24 21:36, , 3F
for suhorng: it's right...
04/24 21:36, 3F
→
04/24 21:47, , 4F
f'(t)/|f(t)| - f(t) (f'(t)．f(t) / |f(t)|^{3/2})?
04/24 21:47, 4F
→
04/24 21:49, , 5F
I am not sure, but how did you get it?
04/24 21:49, 5F
推
04/24 21:53, , 6F
[f(t)g(t)]' = f'(t)g(t) + f(t)g'(t)
04/24 21:53, 6F
→
04/24 21:54, , 7F
d/dt |f(t)| = d/dt √f(t)．f(t)
04/24 21:54, 7F
→
04/24 21:54, , 8F
= [f(t)．f(t)]' / 2√f(t)．f(t)
04/24 21:54, 8F
→
04/24 21:54, , 9F
[f(t)．f(t)]' = 2f(t)．f'(t)
04/24 21:54, 9F
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