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Mathematics

The Chain Rule Beyond One Dimension: Understanding Gradients

Quick fact

The gradient vector, built from partial derivatives, points exactly in the direction of the steepest ascent on a surface—a key idea used in machine learning to minimize errors.

Why this is interesting

You know how to find the slope of a hill, but what if you're on a mountain with slopes in every direction? How do you find the steepest path? The answer lies in a deceptively simple rule that extends beyond one dimension.