1.2 Calculus for ML

The 20-second answer

Calculus tells a model how changing each parameter changes the loss; backpropagation applies the chain rule efficiently to get all those changes.

Core ideas to retain

• A partial derivative changes one variable while holding the rest fixed. The gradient collects all partial derivatives.
• The gradient points uphill; gradient descent moves in $-\nabla L$: $\theta \leftarrow \theta-\eta\nabla L$.
• The chain rule multiplies local derivatives along a path. Backprop reuses this from the output loss back to every weight.
• A Jacobian is first derivatives of a vector output; a Hessian is second derivatives of a scalar loss and describes curvature.

Interview / OA rule

In a derivative OA question, draw the computation graph, work backward, and multiply the local derivative by the upstream gradient. Check the resulting gradient shape.

One good written resource

3Blue1Brown — Essence of Calculus — read this after the video when you want a clearer mental model, not more pages of notes.