 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2008/f/f1/a/solution

For

f = (f_{1}, \dots, f_{k})

, the Jacobian matrix is the matrix of its derivative in standard bases, with entries

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

. Here

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

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