JSFiddle - React, Tailwind, and code Playground

HTML

<script type="text/javascript">
    function calcular() {
        var soma = $('.calcular').get().reduce(function(soma, el) {
            return (parseInt(el.value, 10) || 0) + soma;
        }, 0);
        document.getElementById('result').value = soma;
    }

</script>
<form method="post" action="salvar.php">
    <table class="table table-hover table-bordered">
        <header class="row">
            <h2 class='text-center text-primary'>Pesquise o responsável</h2>
        </header>
        <div class="row">
            <div class="form-group col-md-6 col-md-offset-3">
                <input type="text" class="form-control" id="busca" placeholder="Informe o nome do responśavel">
            </div>
        </div>
        <header class="row">
            <h2 class='text-center text-danger'>Detalhes do Responsável</h2>
        </header>
        <br>
        <div class="row">
            <div class="form-group col-md-2">
                <label for="titulo">Identificação:</label>
                <input type="text" class="form-control" name="identificacao" id="codigo_barra" readonly>
            </div>
            <div class="form-group col-md-4">
                <label for="titulo">Nome Completo:</label>
                <input type="text" class="form-control" name="responsavel" id="titulo_livro" readonly>
            </div>
            <div class="form-group col-md-3">
                <label for="titulo">Valor:</label>
                <input type="text" class="form-control calcular" value="0" id="txt1" name="responsavel" onkeyup="calcular()">
            </div>
            <div class="form-group col-md-3">
                <label for="titulo">Valor Total:</label>
                <input type="text" class="form-control" name="responsavel" id="result" readonly>
            </div>
        </div>
    </table>
    <hr />
    <header class="row">
        <h2 class='text-center text-primary'>Cadastro de Dependentes</h2>
    </header>
    <hr />
    <table id="products-table"...

JavaScript

var AddTableRow = function(el) {
     var tbody = $(el).closest('table').find('tbody');
     var row = tbody.find('tr:last').clone();
     var name = row.find('.calcular').attr('name');
     var index = parseInt(name.match(/usuarios\[(\d+)\]\[valor\]/)[1], 10) + 1;
     row.find('.calcular').attr('name', 'usuarios[' + index + '][valor]');
     tbody.append(row);
 };