class Nested extends React.Component {

  constructor(props){

    super(props);

    this.state = {foo: undefined};

  }

  render() {

    console.log("Rendered " + this.props.name);

    return <div><button onClick={() => {this.setState({foo: Date.now()})}}>Update {this.props.name}</button>{this.props.children ? React.cloneElement(React.Children.only(this.props.children), {foo: this.state.foo}) : undefined}</div>

  }

  componentDidUpdate() {

    console.log("Updated " + this.props.name);

  }

}

​

ReactDOM.render(<Nested name="outer"><Nested name="inner"></Nested></Nested>, document.getElementById("app"));