设 f ( x ) f(x) f(x) 在点 x x x 二阶可导,则:
- 若取点 x , x + Δ x x, x + \Delta x x,x+Δx 的值的差分作为导数的近似值,则:
f ( x + Δ x ) = f ( x ) + f ′ ( x ) Δ x + o ( Δ x ) f(x + \Delta x) = f(x) + f'(x) {\Delta x} + o \left ({\Delta x} \right ) f(x+Δx)=f(x)+f′(x)Δx+o(Δx)
   ⟹    \implies ⟹
f ′ ( x ) = f ( x + Δ x ) − f ( x ) Δ x + o ( 1 ) f'(x) = \dfrac {f(x + \Delta x) - f(x)} {\Delta x} + o(1) f′(x)=Δxf(x+Δx)−f(x)+o(1)
   ⟹    \implies ⟹