函数连续，原函数连续且可导
\(\phi(x + \bigtriangleup x)\) = \(\int_{a}^{x + \bigtriangleup x}\)dt
- $\bigtriangleup \phi = \phi(x + \bigtriangleup x) - \phi (x) $
- = $\int_{a}^{x + \bigtriangleup x} f(x)dt - \int_{a}^{x}f(x) dt $
- = $\int_{a}^{x + \bigtriangleup x} f(x)dt + \int_{x}^{a}f(x) dt $
- = \(\int_{x}^{x + \bigtriangleup x} f(x)dt\)
根据牛顿-莱布尼兹公式：\(\int_{x}^{x + \bigtriangleup x} f(x)dt = \phi(x + \bigtriangleup x) - \phi (x)\)
根据拉格朗日中值定理
\(\phi(x + \bigtriangleup x) - \phi (x) = \phi(\xi) * \bigtriangleup x\)
=>\(\bigtriangleup \phi = f(\xi) \bigtriangleup x\)
=> \(\frac {\bigtriangleup \phi}{\bigtriangleup x} = f(\xi)\)