[autodiff] Take programming's text, so both series publish one lecture

[mmcky]

Makes autodiff one lecture that programming and JAX both publish: this copy becomes programming's text. QuantEcon/lecture-python-programming#644 changes the one sentence that differs there. John and Matt decided this on 2026-10-12 (QuantEcon/project-monorepo#111).

Why. Programming's copy is John's April 2026 adaptation of this lecture (QuantEcon/lecture-python-programming#513), and its corrections never reached this copy. From now on a change is made once and reaches both series.

What changes for readers of this series.

• Corrections: "causes" → "cause", "evalute" → "evaluate", "evaluates" → "evaluate", "my minimizing" → "by minimizing", "auto diff" → "autodiff", and the notation in the $f(x) = \exp(2x)$ example.
• The regression example splits the random key into x_key and ϵ_key before drawing, rather than drawing x with key and then splitting it. The simulated data therefore change, and so do the numbers in that section's output.
• The opening: "This lecture gives an introduction to automatic differentiation using Google JAX" (it said "a brief introduction"), and "Automatic differentiation can be used not only …" (it said "As we will see in later lectures, automatic differentiation …").
• The imports include sympy.symbols, at the top.
• The set-up cell is !pip install jax with its output hidden, in place of the !nvidia-smi GPU check. Here it is a no-op, since CI installs jax[cuda13].

For John:

1. The opening sentence: the wording is a proposal, shared with [autodiff] Open with a sentence that suits both series lecture-python-programming#644.
2. The set-up cell: this takes programming's form and drops the GPU check. 17 of this series' 33 lectures start with !nvidia-smi. One text could carry it too, but a programming reader without a GPU would then see "command not found".

Links in. jax_intro_jax, newtons_method and jax_nn link to this lecture; its name does not change.

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Commit: c27bb7f

📚 Changed Lectures

• autodiff

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Build Info

• Workflow: Build Preview [using jupyter-book]

[Copilot]

🟢 Approval recommended

The changes are verified editorial corrections and a self-consistent random-key refactor with no stored outputs or broken references.

0 open findings

What changed in this PR

This PR syncs lectures/autodiff.md with the programming series' copy (QuantEcon/lecture-python-programming#644) so that a single source serves both the JAX and programming lecture series. The changes are editorial corrections, a setup-cell swap, and a change to how the regression example seeds its random data.

Changes:

• Applies spelling/grammar fixes ("causes"→"cause", "evalute"→"evaluate", "evaluates"→"evaluate", "my minimizing"→"by minimizing", "auto diff"→"autodiff") and fixes the LaTeX notation in the $f(x)=\exp(2x)$ example.
• Replaces the !nvidia-smi GPU check with a hidden-output !pip install jax setup cell and moves from sympy import symbols into the top imports (dropping the now-unused diff import, since .diff() is used as a method).
• Reworks the regression example to split the key into x_key and ϵ_key up front, changing the simulated data (and resulting output numbers), plus softens the opening sentence wording.

File	Description
lectures/​autodiff.md	Editorial corrections, setup-cell swap (pip install jax vs nvidia-smi), import reorganization, and a revised random-key split in the regression example.

🧠 Review effort: Balanced

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