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Задать вопрос экспертам

Консультация № 160167

11.02.2009, 09:51

0.00 руб.

0 1 1

Образование

Здравсвуйте ещё раз мои доргоие эксперты
Помогите решить мне последнюю задачу:

266. Даны функция z=f(x;y), точка A(x0;y0) и вектор а(a1;a2). Найти:
1) grad z в точке A
2) производную в точке A по направлению вектора a
z=arctg(xy^2) A(2;3), a(4;-3).

Обсуждение

Неизвестный

13.02.2009, 12:42

общий

это ответ

Здравствуйте, Мария Романова!
z=arctg(xy²)
1) grad z=dz/dx*i+ dz/dy*j
dz/dx=y²/(1+x²y⁴)
dz/dy=2xy/(1+x²y⁴)
grad z=y²/(1+x²y⁴) * i + 2xy/(1+x²y⁴) * j
grad z(A)=9/(1+324) * i + 12/(1+324) * j=i*9/325 +j*12/325
grad z(A) (9/325, 12/325)

2) gradz(A)*a=9/325 * 4 + 12/325 * (-3)=36/325 - 36/325=0

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