Re: [微分] 一題關於微分
※ 引述《n0204159 (我期待有一天我會回來)》之銘言：
: 2
: g'(x)= [g(x)] + 1 g(0)= 0 g(x) = ?
: g(x+h)-g(x)
: 我由微分的定義做 g'(x) = lim -------
: h→0 h
: g(0+h)-g(0)
: g'(0) = lim -------
: h→0 h
: = lim g(h)
: h→0 ---------
: h
: 2
: = 0 + 1 = 1
: 之後我就完全卡住了...
: 請大大指點一下吧!!
: 謝謝!!
dg/dx = g^2 + 1
=> dg/(1+g^2) = dx
arctan(g(x))-arctan(g(0)) = x - 0
=> arctan(g(x)) = x
=> g(x) = tanx
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 122.124.101.131
→
10/13 23:20, , 1F
10/13 23:20, 1F
推
10/13 23:34, , 2F
10/13 23:34, 2F
推
10/13 23:59, , 3F
10/13 23:59, 3F
推
10/14 09:59, , 4F
10/14 09:59, 4F
→
10/14 10:00, , 5F
10/14 10:00, 5F
→
10/14 10:00, , 6F
10/14 10:00, 6F
推
10/14 13:07, , 7F
10/14 13:07, 7F
推
10/14 20:15, , 8F
10/14 20:15, 8F
討論串 (同標題文章)