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MATH-C06-C-001

Compute change in y divided by change in x.

Substitute x = 5 into 2x.

Use Delta f approx f'(x) Delta x.

When differentiating with respect to x, treat y as constant.

Use [2x, 2y].

Gradient descent uses the negative gradient.

Use the dot product.

Rows correspond to outputs; columns correspond to inputs.

Multiply the local rates.

When one value affects the loss through multiple paths, add the contributions.

The derivative was measured at one point. Local linear estimates are safest for small moves near that point.

Plain gradient descent moves opposite the gradient.

Use Delta f approx J Delta x. Rows are outputs; columns are inputs.

Backprop multiplies upstream sensitivity by the local derivative on that path.