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Консультация № 87798
20.05.2007, 20:34
0.00 руб.
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здравствуйте! помогите пожалуста решить пример:
Для функции u=u(x,y,z) найти значение d^2u/dxdu в точке А.
u=4zcos(xy+1)-(y/x^2)+e, A(-1/2,2,2)
Для функции u=u(x,y,z) найти значение d^2u/dxdu в точке А.
u=4zcos(xy+1)-(y/x^2)+e, A(-1/2,2,2)
Обсуждение
Неизвестный
20.05.2007, 21:11
общий
это ответ
Здравствуйте, Spyro!
Найдем частную производную <i>du/dx</i>:
du/dx = (4zcos(xy+1)-(y/x<sup>2</sup>)+e)‘<sub>x</sub> = 4z*(-sin(xy+1))*(xy+1)‘<sub>x</sub> + (-y/x<sup>2</sup>)‘<sub>x</sub> = -4z*sin(xy+1)*y - (-2xy/x<sup>4</sup>) = -4z*sin(xy+1)*y +2y/x<sup>3</sup>.
И соответственно от результата найдем производную по <i>y</i>:
d<sup>2</sup>u/dxdy = (-4z*sin(xy+1)*y)‘<sub>y</sub> + (2y/x<sup>3</sup>)‘<sub>y</sub> = -4z*cos(xy+1)*xy -4z*sin(xy+1) + 2/x<sup>3</sup>
Осталось только подставить координаты точки:
d<sup>2</sup>u/dxdy(А) = -4*2*cos(-1+1)*(-1) -4*2*sin(-1+1) + 2/(-1/2)<sup>3</sup> = 8*cos(0) - 8*sin(0) + 2/(-1/8) = 8 - 16 = -8.
Good Luck!!!
Найдем частную производную <i>du/dx</i>:
du/dx = (4zcos(xy+1)-(y/x<sup>2</sup>)+e)‘<sub>x</sub> = 4z*(-sin(xy+1))*(xy+1)‘<sub>x</sub> + (-y/x<sup>2</sup>)‘<sub>x</sub> = -4z*sin(xy+1)*y - (-2xy/x<sup>4</sup>) = -4z*sin(xy+1)*y +2y/x<sup>3</sup>.
И соответственно от результата найдем производную по <i>y</i>:
d<sup>2</sup>u/dxdy = (-4z*sin(xy+1)*y)‘<sub>y</sub> + (2y/x<sup>3</sup>)‘<sub>y</sub> = -4z*cos(xy+1)*xy -4z*sin(xy+1) + 2/x<sup>3</sup>
Осталось только подставить координаты точки:
d<sup>2</sup>u/dxdy(А) = -4*2*cos(-1+1)*(-1) -4*2*sin(-1+1) + 2/(-1/2)<sup>3</sup> = 8*cos(0) - 8*sin(0) + 2/(-1/8) = 8 - 16 = -8.
Good Luck!!!
Форма ответа
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