IDZ 10.1 - Option 15. Decisions Ryabushko AP

1. Find the domain of these functions.
1.15 z = ln (y2 - x2)
 
2. Find the partial derivatives and partial differentials of the following functions.
2.15 z = ctg (3x - 2y)

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
3.15 f (x, y, z) = 1 / √x2 + y2-z2, M0 (1, 2, 2)

4. Find the total differentials of these functions.
4.15 z = tg ((x + y) / (x - y))

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.
5.15 u = x / y, x = et, y = 2 - e2t, 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.