| 反函数的导数定理的一个注记 |
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| 引用本文： | 刘孝书. 反函数的导数定理的一个注记[J]. 兵团教育学院学报, 2004, 14(3): 29-30 |
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| 作者姓名： | 刘孝书 |
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| 作者单位： | 商丘师范学院数学系,河南,商丘,476000 |
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| 摘 要： | 给出反函数的导数定理的改进形式:若f(x),x∈(a,b)与φ(y),y(A,B)互为反函数,x0∈(a,b),y0=f(x0),φ(y)在点y0处可导且φ′(y)≠0,f(x)在点x0处连续,则f(x)在点x0处可导,且f′(x0)=1/φ′(y0).并说明,f(x)在点x0处连续这一条件不可去掉。
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| 关 键 词： | 反函数 导数 连续 |
| 文章编号： | 1009-1548(2004)03-0029-02 |
| 修稿时间： | 2004-07-08 |
A Note in the Inverse Function's Derivative Theorem |
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| Liu xiao-shu. A Note in the Inverse Function's Derivative Theorem[J]. Journal of Bingtuan Education Institute, 2004, 14(3): 29-30 |
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| Authors: | Liu xiao-shu |
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| Abstract: | The theorem of the improved inverse function's derivative is presented.If, and are inverse functions to each other, are differential at the point is continuous at the point,and then is differential with.The condition that is continuous at the point can not be omitted. |
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| Keywords: | inverse function derivative continuous |
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