若y=tan^2(x),證明d^2y/dx^2=2(1+y)(1+3y)
嘩,呢題d第二次就計唔岩答案
計唔到既二階導數問題.
2007-11-06 4:45 am
回答 (1)
2007-11-06 4:54 am
✔ 最佳答案
y= tan^2 (x) dy/dx = 2tanx sec^2 (x)
d^2y/dx^2 = 2sec^2 (x) (sec^2 (x)) + 2tanx [2sec(x) * sec(x) tan(x)]
= 2 sec^4 (x) + 4 sec^2 (x) tan^2(x)
= 2sec^2 (x) [ sec^2(x) + 2 tan^2 (x)]
= 2(1+y)(1+y+2y) [Note that sec^2 (x) = 1 + tan^2 (x) = 1+y]
= 2(1+y)(1+3y)
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071105000051KK09327