1. Find the domain of these functions.
1.1 z = 3xy / (2x - 5y)

2. Find the partial derivatives and partial differentials of the following functions.
2.1 z = ln (y2 - e-x)

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
3.1 f (x, y, z) = z / √x2 + y2, M0 (0, -1, 1)

4. Find the total differentials of these functions.
4.1 z = 2x3y - 4xy5

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.
5.1 u = ex - 2y, x = sint, y = t3, t0 = 0

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

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