- Question:
- Evaluate
3
*x*d*x*+ 4*x*^{2}*y*d*y*at (*x*,*y*) = (2, 6) along ⟨d*x*, d*y*⟩ = ⟨0.003, 0.005⟩. - Solution:
- (3
*x*d*x*+ 4*x*^{2}*y*d*y*)|_{(x, y)=(2, 6), ⟨dx, dy⟩=⟨0.003, 0.005⟩}= 3(2)(0.003) + 4(2)^{2}(6)(0.005) = 0.498.

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