# Backpropagate through tanh

> ML Prep screening item.

- Stable ID: `ml-screen-neural-networks-standard-backprop`
- Collection: screening
- Area: Machine Learning
- Topic: Neural Networks
- Origin: original
- Difficulty: medium
- Expected time: 7 minutes
- Skills: forward-pass, activations, neural-network-chain-rule, backpropagation, neural-network-losses
- Item JSON: https://mlprep.iwase.dev/item/ml-screen-neural-networks-standard-backprop.json

## Problem

A scalar network has $h=\tanh(wx)$, $\hat{y}=vh$, and $L=\frac{1}{2}(\hat{y}-y)^2$. At $x=1$, $w=0$, $v=2$, and $y=1$, compute the forward pass, $\frac{\partial L}{\partial v}$, and $\frac{\partial L}{\partial w}$.


## 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 `ml-screen-neural-networks-standard-backprop`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.