**Core Concept**
The derivative of midgut refers to the embryological origin of a particular organ or structure from the midgut region of the developing gastrointestinal tract. The midgut is one of the three main divisions of the embryonic gut, which also includes the foregut and hindgut.

**Why the Correct Answer is Right**
The appendix is a small, tube-like structure attached to the base of the caecum, which is the beginning of the large intestine. During embryonic development, the midgut grows and rotates, and the caecum and appendix develop from the distal portion of the midgut. The appendix is a vestigial remnant of the embryonic caecum, which was involved in the breakdown of yolk sac remnants. The correct development of the midgut and its derivatives is crucial for the proper formation of the gastrointestinal tract.

**Why Each Wrong Option is Incorrect**
**Option A:** The rectum is derived from the hindgut, which is a separate embryological division of the gastrointestinal tract. The hindgut gives rise to the distal one-third of the transverse colon, the descending colon, the sigmoid colon, and the rectum.
**Option C:** The liver is derived from the endoderm of the foregut, specifically the hepatic diverticulum. The liver develops from the foregut endoderm, which also gives rise to the biliary system and the pancreas.
**Option D:** The stomach is also derived from the foregut, specifically the foregut endoderm. The stomach develops from a ventral outpouching of the foregut, which eventually gives rise to the stomach, the proximal duodenum, and the liver.

**Clinical Pearl / High-Yield Fact**
Knowing the embryological origin of organs and structures is essential for understanding congenital anomalies, developmental disorders, and surgical procedures. The midgut derivatives, including the appendix, caecum, and ascending colon, are prone to certain types of anomalies, such as midgut volvulus and malrotation.

✓ Correct Answer: B. Appendix