dns in Dockercontainer not working with vue.js and node: Error: getaddrinfo ENOTFOUND db - node.js

Question

I created a vue.js app which I know try to dockerize.
As Backend I'm using node.js for api calls, which is using mysql as a database.
So I try to create an ui container, a db container, and also a container for nginx.
When trying to create these via docker-compose up --build, I get the following error.
Does anybody know what is the problem here?
$ vue-cli-service build
- Building for production...
events.js:187
throw er; // Unhandled 'error' event
^
Error: getaddrinfo ENOTFOUND db
at GetAddrInfoReqWrap.onlookup [as oncomplete] (dns.js:60:26)
--------------------
at Protocol._enqueue (/app/node_modules/mysql/lib/protocol/Protocol.js:144:48)
at Protocol.handshake (/app/node_modules/mysql/lib/protocol/Protocol.js:51:23)
at Connection.connect (/app/node_modules/mysql/lib/Connection.js:116:18)
[...]
at processTicksAndRejections (internal/process/task_queues.js:80:21) {
errno: 'ENOTFOUND',
code: 'ENOTFOUND',
syscall: 'getaddrinfo',
hostname: 'db',
fatal: true
}
error Command failed with exit code 1.
info Visit https://yarnpkg.com/en/docs/cli/run for documentation about this command.
ERROR: Service 'ui' failed to build: The command '/bin/sh -c yarn run build' returned a non-zero code: 1
This is my docker-compose.yml
version: '3'
networks:
app-tier:
services:
db:
image: mysql:5.7
volumes:
- ./sql:/docker-entrypoint-initdb.d
restart: always
networks:
- app-tier
environment:
- MYSQL_USER=user
[...]
ports:
- 3306:3306
ui:
build: ./ui
container_name: ui
restart: always
networks:
- app-tier
expose:
- 80
ports:
- 3000:3000
[...]
This .ui/Dockerfile
# build stage
FROM node:12.14.0-alpine as build-stage
[...]
# RUN yarn server
RUN yarn run build
# Production stage
FROM nginx:1.16.1-alpine as production-stage
COPY --from=build-stage /app/dist /usr/share/nginx/html
[...]
This is ./ui/src/server/db.js:
const mysql = require('mysql');
const connection = mysql.createConnection({
host: 'db',
user: 'root',
password: 'password',
database: 'dbname',
port: '3306'
});
connection.connect();
module.exports = connection;