IDZ 10.1 - Option 30. Decisions Ryabushko AP

1. Find the domain of these functions.
1.30 z = 4xy / (x2 - y2)
 
2. Find the partial derivatives and partial differentials of the following functions.
2.30 z = e- (x3 + y3)

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
3.30 f (x, y, z) = arcsin (x√y) - yz2, M0 (0, 4, 1)

4. Find the total differentials of these functions.
4.30 z = arctg (2x - 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.
5.30 u = arctg (xy), x = t + 3, y = et, 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.
6.30 z2 = xy - z + x2 - 4, M0 (2, 1, 1)