How to export one cell of a jupyter notebook?

You can register a new cell magic, for example:

from IPython.core.magic import register_cell_magic
@register_cell_magic
def run_and_save(line, cell):
    'Run and save python code block to a file'
    with open(line, 'wt') as fd:
        fd.write(cell)
    code = compile(cell, line, 'exec')
    exec(code, globals())

Now, you can use the run_and_save magic:

%%run_and_save hello.py

class Hello:
   def __init__(self):
      pass

One way this can be done is to use Python's output caching system to access the output of a cell so it can be saved off to a file. The output from a numbered cell x is stored in a variable named _x, and output from the last command is in _ etc. e.g. Save the output of cell number 10 to a file cell_10.pickle using python's pickle format:

import pickle
with open('cell_10.pickle', 'wb') as f:
    pickle.dump(_10, f, pickle.HIGHEST_PROTOCOL)

See this stack question

You can use %%capture Jupyter notebook' magic command to catch output of cell and then paste it to your text file with

with open('output.txt', 'w') as out:
   out.write(cap.stdout)

if you want to cell code to specific file for example code.txt you can use magic function %%writefile

%%writefile example.txt
ab = 'This is code'
a = 5
print(a+ 2)

Also if you want to append to file you must use -a parameter

I am not sure if it is possible to export only one cell in Jupyter notebooks.

But I do know that you could download as a python file and simply copy paste the particular cell you want in your new Jupyter notebook.

Let me know if you need any more help!