Detailed solution for Problem Set 11 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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