C# : 'is' keyword and checking for Not

if(!(child is IContainer))

is the only operator to go (there's no IsNot operator).

You can build an extension method that does it:

public static bool IsA<T>(this object obj) {
    return obj is T;
}

and then use it to:

if (!child.IsA<IContainer>())

And you could follow on your theme:

public static bool IsNotAFreaking<T>(this object obj) {
    return !(obj is T);
}

if (child.IsNotAFreaking<IContainer>()) { // ...

---

Update (considering the OP's code snippet):

Since you're actually casting the value afterward, you could just use as instead:

public void Update(DocumentPart part) {
    part.Update();
    IContainer containerPart = part as IContainer;
    if(containerPart == null) return;
    foreach(DocumentPart child in containerPart.Children) { // omit the cast.
       //...etc...

You can do it this way:

object a = new StreamWriter("c:\\temp\\test.txt");

if (a is TextReader == false)
{
   Console.WriteLine("failed");
}

This hasn't been mentioned yet. It works and I think it looks better than using !(child is IContainer)

if (part is IContainer is false)
{
    return;
}

New In C# 9.0

https://devblogs.microsoft.com/dotnet/welcome-to-c-9-0/#logical-patterns

if (part is not IContainer)
{
    return;
}