1. Find the domain of these functions.

1.28 z = evx2 + y2-1


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

2.28 z = cos (xy) / (x2 + y2)


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

3.28 f (x, y, z) = vx2 + y2-2xycosz, M0 (3, 4, ? / 2)


4. Find the total differentials of these functions.

4.28 z = 7x - x3y2 + y4


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.

5.28 u = arctg (x + y), x = t2 + 2, y = 4 - t2, 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.

6.28 lnz = x + 2y - z + ln3, M0 (1, 1, 3)

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