Why a Surface's Steepness Depends on Direction: Partial Derivatives Explained
TinfoilTricorn · x · 2026-10-06
An intuitive explainer on partial derivatives: for a surface z = f(x, y), ∂f/∂x is the rate of change when only x varies with y held fixed, while ∂f/∂y does the opposite. These correspond to the slopes of two curves (blue and red) on the surface, explaining why steepness depends on the direction you walk.
The author then connects this to machine learning: backpropagation differentiates the loss with respect to each weight while others stay constant, and every gradient-descent step is built from these partial derivatives.
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