This is the 4501st most frequent Russian word.
выводить
"To lead out," "to bring out," or "to derive."
In this sentence, 'вывожу' refers to taking out someone/something to another location for a purpose, like going for a walk.
Я вывожу вашу собаку на прогулку каждый вечер.
I take your dog for a walk every evening.
'выведению' here is used in the sense of extracting or bringing out substances or elements from within something.
Эта программа способствует выведению токсинов из организма.
This program facilitates the removal of toxins from the body.
In this context, 'выводит' means causing someone to experience frustration or to lose their temper due to certain actions or statements.