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Консультация № 108927
Обсуждение
Неизвестный
11.11.2007, 13:09
общий
это ответ
Здравствуйте, Kamelia26!
y‘=arccos(x/3) + x*(-1/(3*√(1-(x^2/9)) + (2x)/(2√(9-x^2))=
=arccos(x/3)- x/√(9-x^2) + x/√(9-x^2)=arccos(x/3)
y‘=arccos(x/3) + x*(-1/(3*√(1-(x^2/9)) + (2x)/(2√(9-x^2))=
=arccos(x/3)- x/√(9-x^2) + x/√(9-x^2)=arccos(x/3)
Неизвестный
11.11.2007, 13:21
общий
это ответ
Здравствуйте, Kamelia26!
Для наглядности, продифференцируем каждое слагаемое отдельно.
[x*arccos(x/3)]‘ = (x)‘*arccos(x/3) + x*(arccos(x/3))‘ = arccos(x/3) - (x/3)/√(1-(x²/9)) = arccos(x/3) - x/√(9-x²)
(√(9-x²))‘ = -x/√(9-x²)
=> производная всей функции y‘ = arccos(x/3) - x/√(9-x²) + x/√(9-x²) = arccos(x/3)
Для наглядности, продифференцируем каждое слагаемое отдельно.
[x*arccos(x/3)]‘ = (x)‘*arccos(x/3) + x*(arccos(x/3))‘ = arccos(x/3) - (x/3)/√(1-(x²/9)) = arccos(x/3) - x/√(9-x²)
(√(9-x²))‘ = -x/√(9-x²)
=> производная всей функции y‘ = arccos(x/3) - x/√(9-x²) + x/√(9-x²) = arccos(x/3)
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