public class Derived2Validator : AbstractValidator<Derived2>
{
    public Derived2Validator()
    {
        Include(new BaseValidator());
        Include(new Derived1Validator());
        RuleFor(d => d.Derived1Name).NotNull();
    }
}

Derived2Validator does not need to inherit BaseValidator or Derived1Validator.

Use the Include method to include the rules from other validators.

One approach to take would be as follows:

public class Base
{
    public string BaseName { get; set; } 
}

public class Derived1 : Base
{
    public string Derived1Name { get; set; }
}

public class BaseValidator<T> : AbstractValidator<T> where T : Base
{
    public BaseValidator()
    {
        RuleFor(b => b.BaseName).NotNull();
    }
}

public class Derived1Validator : BaseValidator<Derived1>
{
    public Derived1Validator()
    {
        RuleFor(d => d.Derived1Name).NotNull();
    }
}

So you first create your base validator, make it accept a generic type argument and specify that the generic type must be of type base. Set up your general rules for your base class and move on.

For any validators that validate children of your base class, you have those validators inherit from the baseValidator, where T will be your derived class type.

I tried the Include() method, but that did not give me desired results as models generated by swagger in .net core did not show any changes. what did work was creating a new class to inherit from for validators that have a base class

/// <summary>
/// Base Class for entity validator classes that specifies a base validator class
/// </summary>
/// <typeparam name="T">The Type being validated</typeparam>
/// <typeparam name="TBaseClass">The validater assigned to the base type of the type being validated</typeparam>
public abstract class BaseAbstractValidator<T, TBaseClass> : AbstractValidator<T>
    where TBaseClass : IEnumerable<IValidationRule>
{
    protected BaseAbstractValidator() => AppendRules<TBaseClass>();

    /// <summary>
    /// Add the set of validation rules
    /// </summary>
    /// <typeparam name="TValidationRule"></typeparam>
    private void AppendRules<TValidationRule>() where TValidationRule : IEnumerable<IValidationRule>
    {
        var rules = (IEnumerable<IValidationRule>)Activator.CreateInstance<TValidationRule>();
        foreach (var rule in rules)
        {
            AddRule(rule);
        }
    }
}