Detailed solution for Problem Set 7 (non-textbook part) Exercise 5
- Question:
- Evaluate d(2xy + 3x2)
at (x, y) = (2, 3).
- Solution:
- d(2xy + 3x2)|(x, y)=(2, 3) =
(d(2xy) + d(3x2))|(x, y)=(2, 3) =
(2 d(xy) + 3 d(x2))|(x, y)=(2, 3) =
(2(y dx + x dy) + 3(2x2−1 dx))|(x, y)=(2, 3) =
2((3) dx + (2) dy) +
6(2) dx =
6 dx + 4 dy + 12 dx =
18 dx + 4 dy.
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