ИДЗ 10.1 – Вариант 2. Решения Рябушко А.П.

1. Find the domain of these functions.

1.2 z = arcsin (x - y)

2. Find the partial derivatives and partial differentials of the following functions.

2.2 z = arcsinvxy

3. Calculate the value of partial f´x (M0), f´y (M0), f´z (M0), for the function f (x, y, z) at the point M0 (x0, y0, z0) with an accuracy of to two decimal places

3.2 f (x, y, z) = ln (x + y / 2z), M0 (1, 2, 1)

4. Find the total differentials of these functions.

4.2 z = x2ysinx - 3y

5. Calculate the value of the derivative of a composite function u = u (x, y), where x = x (t), y = y (t), at t = t0 up to two decimal places.

5.2 u = ln (ex + e-y), x = t2, y = t3, t0 = -1

6. Calculate the values \u200b\u200bof the partial derivatives of the function z (x, y) given implicitly at the point M0 (x0, y0, z0) accurate to two decimal places.

6.2 x2 + y2 + z2 - xy = 2, M0 (-1, 0, 1)

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