Question

how to write essay in japanese

Answer 1

The basic rule of thumb is ~である form for anything academic, official, or the newspaper, ~だ form for anything formal but not wanting to sound as rigid as
~である, and ~です/ます form for more personal essays where you want the reader to feel as if the writer is addressing them, such as "letters to the editor" or essays meant to be spoken (documentaries, memoirs, eulogies, talks).

However there is overlap. In the end it depends on the type of impression you want to give with the piece of writing.

It's important not to mix forms without reason, however, *technically speaking* there are instances where both are used in one essay:
Technicalities like direct quoting, or when the title is in a different form than the essay, or if an essay includes a list of items (lists are generally だ form)
Sometimes in a だ form essay you can use である for one sentence you want to particularily stress.

In more non-academic essays you may find...
Sometimes in a です/ます form essay you can use a だ form sentence. This is a stylistic choice done to add a rhythmic pause to your writing. (Ex: 私は出汁を自分で作っています。現代人にはそんな手間かかることをする暇がない、本だしでいいでしょうと主張する人が多いかと思います。しかし、便利だからといって、添加物が混ざっているため、昔の味が再現できるとは言い難いです。手間をかけて素材にこだわる。それが、私の譲れない価値観です。)
Finishing a sentence on a noun gives a simlar rhythmic effect, and is possible in both です/ます and だ form essays. (Ex: 震災から４年。地元の団体がまだまだ復興に向けて努力を続けています。)

If you are a student of Japanese and want to practice your academic writing, I would recommend the book series 『大学・大学院 留学生の日本語』published by 株式会社アルク. I used ①読解編 in a college class--you will learn about essay structure and grammar while improving reading comprehension.

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