Bootstrap: How to place button next to input-group

You could also try the pull-left class.

The classes .pull-left and .pull-right also exist and were previously used as part of the media component, but are deprecated for that use as of v3.3.0. They are approximately equivalent to .media-left and .media-right, except that .media-right should be placed after the .media-body in the html.

The html:

<div>
    <div class="pull-left">
        <button type="button" class="btn">Delete</button>
    </div>
    <div>
        <div class="input-group">
            <input type="text" class="form-control" value="1" />
            <span class="input-group-addon">Update</span>
        </div>
    </div>
</div>

You can use:

style="margin-right:5px"

to add some spacing after the div, and then the new mark-up would be as follows:

<div>
    <div class="pull-left" style="margin-right:5px">
        <button type="button" class="btn">Delete</button>
    </div>
    <div>
        <div class="input-group">
            <input type="text" class="form-control" value="1" />
            <span class="input-group-addon">Update</span>
        </div>
    </div>
</div>

With your current code, you can use the flexbox.

A powerful CSS layout module that gives us an efficient and simple way to lay out and align things.

<div class="flex">
   <div>
     <button type="button" class="btn">Delete</button>
   </div>
   <div>
     <div class="input-group">
        <input type="text" class="form-control" value="1" />
        <span class="input-group-addon">Update</span>
     </div>
   </div>
</div>

.flex {
   display: flex;
   flex-direction: row;
}

This is the screenshot of the result:

You can learn more about flexbox here: https://css-tricks.com/snippets/css/a-guide-to-flexbox/

Cheers!