Conclusion: 𝑦+=𝑓(𝑥+)≈y−â∂𝑔∂𝑦y+=f(x+)≈y−a^∂g∂y, where âa^ is some positive scaler. i.e., 𝑦y update along negative gradient. Proof: Calculate the first-order Taylor expansion of 𝑓(𝑥+)f(x+) on 𝑥x: 𝑦+−y=𝑓(𝑥+)−...