Please show complete steps on how to deal with the absolute value symbol
Thanks!!
更新1:
係唔係 f(x) cannot be differentiated at x=0 可不可以用 first derivative rule計
Help me with differentiation!!
2012-11-20 10:16 am
What is the derivative of f(x)= x* abs(x)
Please show complete steps on how to deal with the absolute value symbol
Thanks!!
Please show complete steps on how to deal with the absolute value symbol
Thanks!!
回答 (3)
2012-11-20 10:53 am
✔ 最佳答案
f(x) = x|x|f'(x)
= x(d/dx |x|) + |x| ... (Product rule)
= x(x/|x|) + |x|
= (x^2)/|x| + |x|
= (|x|^2)/|x| + |x|
= |x| + |x|
= 2|x|
Note:
In y = |x|
since |x|^2 = x^2
-> |x| = (x^2)^(1/2)
dy/dx
= [(1/2)(x^2)^(-1/2)](2x)
= x/(x^2)^(1/2)
= x/|x|
i.e. d/dx |x| = x/|x|
參考: Myself
2012-11-21 12:04 am
Math Use Bi 26 Law England Use
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Math Use Bi 23 Putonghua's Use
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Math Use Bi 23 Putonghua's Use
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參考: Math Use Bi Teaching (86) 10
2012-11-20 3:58 pm
case(i), x >= 0,
f(x) = x(x) = x^2 => f '(x) = 2x
case(ii), x < 0,
f(x) = x(-x) = -x^2 => f '(x) = -2x
f(x) = x(x) = x^2 => f '(x) = 2x
case(ii), x < 0,
f(x) = x(-x) = -x^2 => f '(x) = -2x
收錄日期: 2021-04-28 14:21:29
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20121120000051KK00025