JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css">
<div class="container">
  <br/>
  <div class="input-group">
      <input type="text" aria-label="Text input with segmented button dropdown" class="form-control">
      <div class="input-group-btn">
          <button aria-expanded="false" aria-haspopup="true" data-toggle="dropdown" class="btn btn-default dropdown-toggle" type="button">
              <span class="caret"></span>
              <span class="sr-only">Toggle Dropdown</span>
          </button>

          <ul class="dropdown-menu">
              <li><a href="#">Action</a></li>
              <li><a href="#">Another action</a></li>
              <li><a href="#">Something else here</a></li>
              <li class="divider" role="separator"></li>
              <li><a href="#">Separated link</a></li>
          </ul>
          <button class="btn btn-default" type="button">Action</button>
     </div>
 </div>
</div>

CSS

.input-group-btn:last-child > .btn:not(:last-child).dropdown-toggle {
  border-radius: 0;
}