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arctanx的导数是什么

更新时间: 2021-02-24 10:45:48     

1、arctanx的导数是:1/1+x2。

2、设y=arctanx,则x=tany。

因为arctanx′=1/tany′,且tany′=(siny/cosy)′=cosycosy-siny(-siny)/cos2y=1/cos2y。

则arctanx′=cos2y=cos2y/sin2y+cos2y=1/1+tan2y=1/1+x2。

所以arctanx的导数是1/1+x2。

关键词: arctanx 什么

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