Step 1: About Buddhacarita.
Buddhacarita is a classical Sanskrit epic poem that narrates the life of Gautama Buddha.
Step 2: Authorship.
It was composed by the great poet-philosopher Aśvaghoṣa in the 1st–2nd century CE.
Step 3: Analysis of options.
- (1) Buddhaghoṣa: Known for commentaries in Pali, not the Buddhacarita.
- (2) Aśvaghoṣa: Correct author of Buddhacarita.
- (3) Dhammapāla: Wrote commentaries, not this text.
- (4) Buddhadatta: A Theravāda commentator, not the author here.
Step 4: Conclusion.
Thus, the writer of Buddhacarita is **Aśvaghoṣa**.