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arctanx的导数怎么求

arctanx的导数怎么求

y=arctan来自x,则x=tany

arctanx′=1/tany′

tany′=(siny/cosy)′=cosycosy-siny(-siny)/cos²y=1/cos²y

则arctanx′=cos²y=cos²宁外完了医y/sin²y+cos²y=1/1+tan²y=1/1+x²

故最终答案是1/1+x²

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