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Консультация № 161506
26.02.2009, 22:33
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Здравствуйте! Помогите мне пожалуйста найти производную функции: y=sin(2^x)
Заранее спасибо!
Заранее спасибо!
Обсуждение
Неизвестный
26.02.2009, 22:39
общий
это ответ
Здравствуйте, Alenab1227!
y=sin(2^x) => dy/dx=(2^x)*ln2*cos(2^x)
y=sin(2^x) => dy/dx=(2^x)*ln2*cos(2^x)
Неизвестный
26.02.2009, 22:40
общий
это ответ
Здравствуйте, Alenab1227!
y' = cos(2^x) * (2^x)' = cos(2^x) * 2^x * ln2
y' = cos(2^x) * (2^x)' = cos(2^x) * 2^x * ln2
Неизвестный
27.02.2009, 14:36
общий
27.02.2009, 15:23
это ответ
Здравствуйте, Alenab1227!
Вам необходимо найти производную сложной функции.
Формулу вычисления сложной функции можно посмотреть здесь:
http://www.exponenta.ru/educat/class/courses/ma/theme9/theory.asp
Таблицу производных здесь:
для Вашей задачи решение будет таким:
y=sin(2^x)
Пусть u=2^x, тогда y'=sin(u)'=cos(u)*2^x*ln2=cos(2^x)*2^x*ln2
Вам необходимо найти производную сложной функции.
Формулу вычисления сложной функции можно посмотреть здесь:
http://www.exponenta.ru/educat/class/courses/ma/theme9/theory.asp
Таблицу производных здесь:
для Вашей задачи решение будет таким:
y=sin(2^x)
Пусть u=2^x, тогда y'=sin(u)'=cos(u)*2^x*ln2=cos(2^x)*2^x*ln2
Форма ответа
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