Question: Given a unit direction vector v = (v1, ..., va), verify that forward-mode AD computes the directional derivative VS . V = of of Ult

Given a unit direction vector v = (v1, ..., va), verify that forward-mode AD computes the directional derivative VS . V = of of Ult ... + Ud ard by setting the starting values for the forward tangent traces to 21 = v1, ..., I'd = va. (This is why to compute the derivative Of/Or; one needs to set a; = 1 and a; = 0, for j / i.) Verify this by computing the directional derivative along v = (v1, v2) of the example function f(x1, 12) = (2172 + sin x] + 4) (3x2 + 6) at an arbitrary point (21, 12) = (a, b)

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