# Gradient and a normalized direction

> ML Prep screening item.

- Stable ID: `math-calc-02-gradient-direction`
- Collection: screening
- Area: Mathematics
- Topic: Calculus
- Origin: original
- Difficulty: easy
- Expected time: 3 minutes
- Skills: partial-derivatives, gradient, directional-derivative
- Item JSON: https://mlprep.iwase.dev/item/math-calc-02-gradient-direction.json

## Problem

Let $f(x,y)=x^2y+e^y$. Compute $\nabla f(1,0)$ and the directional derivative
there in the direction from $(1,0)$ toward $(4,4)$.


## Answer policy

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## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `math-calc-02-gradient-direction`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.