# Implicit tangent slope

> ML Prep screening item.

- Stable ID: `math-calc-07-implicit-slope`
- Collection: screening
- Area: Mathematics
- Topic: Calculus
- Origin: original
- Difficulty: medium
- Expected time: 3 minutes
- Skills: implicit-differentiation
- Item JSON: https://mlprep.iwase.dev/item/math-calc-07-implicit-slope.json

## Problem

The curve $x^2+xy+y^2=7$ passes through $(1,2)$. Find $dy/dx$ at that point.


## 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-07-implicit-slope`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.