How can I return a derived class instance from a base class function

Let's say I have two classes. base and derived_from_base. base will contain a lot of functions that will control certain aspects of base and the derived classes will use. However, I would like to make it so I can chain calls to these functions.

class data_class {};

class base {
public:
  base* add_data(data_class* data) {
    m_Data = data;
    return this;
  }

private:
  data_class* m_Data;
};

class derived_from_base : public base {
  void custom_function() {}
};

int main() {
  data_class* someData = new data_class();

  // "myClass" has none of the data after this return
  derived_from_base* myClass = derived_from_base().add_data(someData);

  derived_from_base* myOtherClass = derived_from_base();
  // The data is available in this class now.
  myOtherClass.add_data(someData);
}

I have tried passing the derived classes this pointer to the base class but it has yielded the same results.

One way things like this are sometimes accomplished is via the CRTP-idiom.

In your case this would look something like this:

class Base {
private:
  // ...
public:
  Base* add_data(data_class* data) {
    // implementation ...
  }
};

template <typename T>
class BaseCRTP : public Base {
public:
  T* add_data(class_data* data) {
    return static_cast<T*>(Base::add_data(data));
  }
};

class Derived : public BaseCRTP<Derived> {
public:
  void custom_function() {}
};

int main() {
  Derived derived;
  derived.add_data(new class_data())->custom_function();
}

This is not the best style in several points. For one, it would be better to return a reference, not a pointer. So *this, not this.

Anyway, by introducing an intermediate base class template you offload the code-reuse to a template and have to write a wrapper only once.