IDZ 10.1 - Option 7. Decisions Ryabushko AP

1. Find the domain of these functions.
1.7 z = arccos (x + y)

2. Find the partial derivatives and partial differentials of the following functions.
2.7 z = ctg√xy3

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
3.7 f (x, y, z) = 3√x + y + z3, M0 (3, 4, 2)

4. Find the total differentials of these functions.
4.7 z = ln (3x2 - 2y2)

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.
5.7 u = xy, x = et, y = lnt, t0 = 1

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.