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Консультация № 192119
14.12.2017, 10:34
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Здравствуйте! У меня возникли сложности с таким вопросом:
Задана функция z=xsin(x+y)-1. Найти градиент и производную этой функции в заданной точке М(pi/6;pi/6) в направлении вектора , составляющего угол a=pi/4 с положительным направлением оси ОХ. Помогите, пожалуйста
Задана функция z=xsin(x+y)-1. Найти градиент и производную этой функции в заданной точке М(pi/6;pi/6) в направлении вектора , составляющего угол a=pi/4 с положительным направлением оси ОХ. Помогите, пожалуйста
Обсуждение
14.12.2017, 11:10
общий
это ответ
Здравствуйте, Алёна Прокудина!
1) Градиент функции в точке М:
Модуль градиента фунцкии в точке М:
Направление вектора градиента задается его направляющими косинусами:
2) Так как вектор
составляет угол 
с положительным направлением оси 
,
то его направляющие косинусы:
Производная функции в точке М по направлению вектора: 
1) Градиент функции в точке М:
Модуль градиента фунцкии в точке М:
Направление вектора градиента задается его направляющими косинусами:
2) Так как вектор
составляет угол с положительным направлением оси ,то его направляющие косинусы:
Производная функции в точке М по направлению вектора
:
5
Спасибо Вам огромное, очень выручили!
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