# Vector chain rule

> ML Prep screening item.

- Stable ID: `math-calc-03-jacobian-chain`
- Collection: screening
- Area: Mathematics
- Topic: Calculus
- Origin: original
- Difficulty: medium
- Expected time: 4 minutes
- Skills: jacobian, multivariable-chain-rule
- Item JSON: https://mlprep.iwase.dev/item/math-calc-03-jacobian-chain.json

## Problem

Let $F(x,y)=(x^2+y,xy)$ and $h(u,v)=u^2+3v$. Compute $J_F(1,2)$ and
$\nabla(h\circ F)(1,2)$.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `math-calc-03-jacobian-chain`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.