Given that ln（y+5x+2）= x+ln3
If dy/dx =5x+y-3
Show that d^2y/dx^2 =3e^x. Hence find d^2y/dx^2 at the point (0,1)
請問
d^2y/dx^2 怎可以化成3e^x.
Amath 問題
2013-02-07 7:35 am
回答 (2)
2013-02-07 9:20 am
✔ 最佳答案
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參考: pingshek
2013-02-07 9:14 am
concept:
1. A = e^(lnA) = ln(e^A)
2. ln A + ln B = ln(AB)
-----------------------------------
d²y/dx²
= 5 + dy/dx
= 5x+y+2
= exp[ln (5x+y+2)]
= exp[x+ln3]
= exp[ln(e^x)+ln 3]
= exp[ln(3e^x)]
= 3e^x
note: exp[x] means e^x, for clarity
2013-02-07 01:16:12 補充：
or you may say
exp[x+ln3]
= exp[x] * exp[ln 3]
= 3e^x
i think this is better
1. A = e^(lnA) = ln(e^A)
2. ln A + ln B = ln(AB)
-----------------------------------
d²y/dx²
= 5 + dy/dx
= 5x+y+2
= exp[ln (5x+y+2)]
= exp[x+ln3]
= exp[ln(e^x)+ln 3]
= exp[ln(3e^x)]
= 3e^x
note: exp[x] means e^x, for clarity
2013-02-07 01:16:12 補充：
or you may say
exp[x+ln3]
= exp[x] * exp[ln 3]
= 3e^x
i think this is better
收錄日期: 2021-04-25 12:52:40
原文連結 [永久失效]:
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