导数定义公式的一个推广及其应用研究

A Promotion and Research on the Application of Derivative Definition Formula

将导数在某一点的定义f′(x0)=limh→0f(x0+h)-f(x0)/h推广为f′(x0)=limf[x0+α(x)]-f[x0+β(x)]/α(x)-β(x)(α(x)→0,β(x)→0),从而简化了有关导数定义一类问题的求解.

A point definition of derivative is promoted fromf′（x0）=limh→0f（x0＋h）-f（x0）/h to f′（x0）=limf[x0＋α（x）]-f[x0＋β（x）]/α（x）-β（x）（α（x）→0,β（x）→）. Simplified the solution to the relevant problems of deriv-ative defination.