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Консультация № 177284
16.03.2010, 14:15
35.91 руб.
16.03.2010, 14:24
0
1
1
Здравствуйте, уважаемые эксперты!
Найти производную функции, заданной неявно.
Найти производную функции, заданной неявно.
Обсуждение
16.03.2010, 15:38
общий
это ответ
Здравствуйте, sanekvseti.
Для нахождения производной y’ будем дифференцировать обе части заданного в условии равенства, считая, что x – независимая переменная, а y – функция переменной x. Из полученного уравнения найдем y’:
(8x^7)*y^3 + (x^8)*(3y^2)*y’ – 7y’ = -(sin(5x + 2y))*(5 + 2y’),
(8x^7)*y^3 + (x^8)*(3y^2)*y’ – 7y’ = -5*sin(5x + 2y) – 2y’*sin(5x + 2y),
y’*((x^8)*(3y^2) – 7 + 2*sin(5x + 2y)) = -5*sin(5x + 2y) – (8x^7)*y^3,
y’ = (-5*sin(5x + 2y) – 8x^7*y^3)/(3*x^8*y^2 – 7 + 2*sin(5x + 2y)).
Вроде бы так…
С уважением.
Для нахождения производной y’ будем дифференцировать обе части заданного в условии равенства, считая, что x – независимая переменная, а y – функция переменной x. Из полученного уравнения найдем y’:
(8x^7)*y^3 + (x^8)*(3y^2)*y’ – 7y’ = -(sin(5x + 2y))*(5 + 2y’),
(8x^7)*y^3 + (x^8)*(3y^2)*y’ – 7y’ = -5*sin(5x + 2y) – 2y’*sin(5x + 2y),
y’*((x^8)*(3y^2) – 7 + 2*sin(5x + 2y)) = -5*sin(5x + 2y) – (8x^7)*y^3,
y’ = (-5*sin(5x + 2y) – 8x^7*y^3)/(3*x^8*y^2 – 7 + 2*sin(5x + 2y)).
Вроде бы так…
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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