string password_hash ( string $password , integer $algo [, array $options ] )

$check = mysql_query("SELECT `id` FROM `database`.`user`
WHERE `password` = '".$password."'") or die(mysql_error());

$insert = mysql_query("INSERT INTO `database`.`user`(`username`,`password`,`email`)
VALUES ('".$username."','".$password."','".$email."')") or die(mysql_error());

$update = mysql_query("UPDATE `database`.`user` SET `password` = '".$newpassword."'
WHERE `password` = '".$oldpassword."'") or die(mysql_error());

$username = mysql_real_escape_string($_POST['username']);
$password = mysql_real_escape_string($_POST['password']);
$email = mysql_real_escape_string($_POST['email']);

$mysqli = new mysqli( 'enderecodoservidor', 'usuario', 'senha', 'basededados' );

$usuario = $_POST['usuario'];
$hash    = password_hash( $_POST['senha'], PASSWORD_DEFAULT );

$query = 'INSERT INTO usuarios ( nome, hash) VALUES ( ?, ? )';
$stmt = $mysqli->prepare( $query );
$stmt->bind_param("ss", $usuario, $hash );
$stmt->execute();

$mysqli = new mysqli( 'enderecodoservidor', 'usuario', 'senha', 'basededados' );

$usuario = $_session['usuario']; // ou idusuario, depende como voce mantem o login
$hash    = password_hash( $_POST['novaSenha'], PASSWORD_DEFAULT );

$query = 'UPDATE usuarios SET hash= ? WHERE nome = ? '; // ou WHERE id = ?
$stmt = $mysqli->prepare( $query );
$stmt->bind_param("ss", $hash , $usuario ); // ou ("si", $hash, $idUsuario)
$stmt->execute();

$mysqli = new mysqli( 'enderecodoservidor', 'usuario', 'senha', 'basededados' );

$usuario = $_POST['usuario'];
$idUsuario = 0;

$query = 'SELECT id, hash FROM usuarios WHERE nome = ?';
$stmt = $mysqli->prepare( $query );
$stmt->bind_param("ss", $usuario );
$stmt->execute();

$stmt->bind_result( $idUsuario, $hash );
$stmt->fetch();

if ( password_verify( $_POST['senha'], $hash );

$password = password_hash($password);
$check = mysql_query("SELECT `id` FROM `database`.`user`
WHERE `password` = '".$password."'") or die(mysql_error());

$password = password_hash($password);
$insert = mysql_query("INSERT INTO `database`.`user`(`username`,`password`,`email`)
VALUES ('".$username."','".$password."','".$email."')") or die(mysql_error());

$password = password_hash($password);
$oldpassword = password_hash($oldpassword);
$update = mysql_query("UPDATE `database`.`user` SET `password` = '".$newpassword."'
WHERE `password` = '".$oldpassword."'") or die(mysql_error());