General 𝑓′(𝑥)≈𝑐1𝑓(𝑥+ℎ)+𝑐2𝑓(𝑥)+𝑐3𝑓(𝑥−ℎ) by Taylor expansion 𝑓(𝑥+ℎ)=𝑓(𝑥)+ℎ𝑓′(𝑥)+ℎ22!𝑓″(𝑥)+⋯+ℎ𝑛𝑛!𝑓(𝑛)(𝑥) 𝑓(𝑥−ℎ)=𝑓(𝑥)−ℎ𝑓′(𝑥)+ℎ22!𝑓″(𝑥)−⋯+ℎ𝑛𝑛!𝑓(𝑛)(𝑥) Forward difference 𝑓′(𝑥)≈𝑓(𝑥+ℎ)−𝑓(𝑥)ℎ=𝑓′(𝑥)+𝐶ℎ+𝑂(ℎ2) Center difference 𝑓′(𝑥)≈𝑓(𝑥+ℎ)−𝑓(𝑥−ℎ)2ℎ=𝑓′(𝑥)+𝐶ℎ2+𝑂(ℎ4)