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Консультация № 108926
Обсуждение
Неизвестный
11.11.2007, 13:10
общий
это ответ
Здравствуйте, Kamelia26!
Воспользуемся формулой производной суммы и производной сложной функции
y‘=√(9-х²) - x²/√(9-х²) + 3/√(1-х²/9) = 9-х²/√(9-х²) - x²/√(9-х²) + 9/√(9-х²) = 2(9-х²)/√(9-х²) = 2√(9-х²)
Воспользуемся формулой производной суммы и производной сложной функции
y‘=√(9-х²) - x²/√(9-х²) + 3/√(1-х²/9) = 9-х²/√(9-х²) - x²/√(9-х²) + 9/√(9-х²) = 2(9-х²)/√(9-х²) = 2√(9-х²)
Неизвестный
11.11.2007, 13:16
общий
это ответ
Здравствуйте, Kamelia26!
y = x*√(9-x<sup>2</sup>) + 9*arcsin(x/3)
y‘ = (x*√(9-x<sup>2</sup>))‘ + (9*arcsin(x/3))‘ = √(9-x<sup>2</sup>) + x*(-x<sup>2</sup>)‘/(2*√(9-x<sup>2</sup>)) + 9*(x/3)‘/√(1-(x/3)<sup>2</sup>) =
= √(9-x<sup>2</sup>) - x<sup>2</sup>/√(9-x<sup>2</sup>) + 3/√(1-(x/3)<sup>2</sup>) = √(9-x<sup>2</sup>) - x<sup>2</sup>/√(9-x<sup>2</sup>) + 9/√(9-x<sup>2</sup>) = √(9-x<sup>2</sup>) + (9-x<sup>2</sup>/√(9-x<sup>2</sup>) = 2√(9-x<sup>2</sup>).
Good Luck!!!
y = x*√(9-x<sup>2</sup>) + 9*arcsin(x/3)
y‘ = (x*√(9-x<sup>2</sup>))‘ + (9*arcsin(x/3))‘ = √(9-x<sup>2</sup>) + x*(-x<sup>2</sup>)‘/(2*√(9-x<sup>2</sup>)) + 9*(x/3)‘/√(1-(x/3)<sup>2</sup>) =
= √(9-x<sup>2</sup>) - x<sup>2</sup>/√(9-x<sup>2</sup>) + 3/√(1-(x/3)<sup>2</sup>) = √(9-x<sup>2</sup>) - x<sup>2</sup>/√(9-x<sup>2</sup>) + 9/√(9-x<sup>2</sup>) = √(9-x<sup>2</sup>) + (9-x<sup>2</sup>/√(9-x<sup>2</sup>) = 2√(9-x<sup>2</sup>).
Good Luck!!!
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