Question

y＝arctanx的求导过程是什么？

Answer 1

y=arctanx,则x=tany

arctanx′=1／tany′

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

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

故最终答案是1/1+x²

参考资料

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