Slope and the derivative

Slope is rise over run: how much the output changes for each step of the input. A straight line has the same slope everywhere; a curve's slope changes. The derivative gives the slope at each point. For f(x) = x² it is 2x, so at x = 3 the curve climbs 6 units per unit of x, and at the bottom of a valley the slope is 0.

Why it matters: Training uses derivatives to work out which way to nudge each weight.

Builds on: Functions and graphs

Learn it, then prove it

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