 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2008/f/1/a/solution

f : Ω \subset R^{n} \to R^{k}

, the Jacobian matrix represents its derivative and has entries

(D f)_{ij} = \partial f_{i} / \partial x_{j}

. Differentiating the two components gives

D f (x, y) = (e^{x} sin y - e^{- y} sin x e^{x} cos y - e^{- y} cos x) .

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