微積分指數對數函數的導函數

👨🏻‍🏫 學術台數學

[匿名]

2009-06-01 7:16 am

(1)求y=ln(e2x+e-x)根號
(2)y=3右上方放2x
(3)y=ln(x^2+y^2)

更新1:

是整個要根號謝謝

更新2:

(1)答案是你那答案分母少掉那個根號那一串才是答案耶>< (2)y=ln3‧3右上方2x‧ln2‧2右上方x

更新3:

(1)y=ln(e右上方2x+e右上方-x)根號前面ln不用根號

更新4:

答案是 (2)y=ln3‧3右上方2x‧ln2‧2右上方x 跟你不一樣>

回答 (3)

STEVIE-G™

2009-06-01 9:09 am

✔ 最佳答案

As follows:

圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/07-3.gif

2009-06-02 20:08:26 補充：
第一題之修正:
http://i707.photobucket.com/albums/ww74/stevieg90/08-6.gif

2009-06-05 19:55:25 補充：
第二題之修正:
http://i707.photobucket.com/albums/ww74/stevieg90/04-19.gif

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[匿名]

2009-06-01 9:24 am

(1)

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or

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(2)

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or換底

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(3)

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or 直接套用ln微分公式再做移項整理

2009-06-02 20:11:13 補充：
y=ln[(x^2+y^2)^(1/2)]=(1/2)ln(x^2+y^2)
y'=(1/2)[(2x+2y)/(x^2+y^2)]=(x+y)/(x^2+y^2)

2009-06-02 20:13:50 補充：
剛剛補充不小心把根號放到第三題
更改過題目後的第一題為下
y=ln[(e2x+e-x)^(1/2)]=(1/2)ln(e^(2x)+e^(-x))
=(1/2)[(2e^(2x)-e^(-x))/(e^(2x)+e^(-x))]

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[匿名]

2009-06-01 7:23 am

1. 根號是指整個的還是只有 e^(2x)+e^(-x)
2. 3^(2x) ??
3. 是隱微分?? 想確定一下!!

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收錄日期: 2021-04-22 00:48:02
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090531000015KK11554

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