 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2011/f/f2/a/ii/solution

\nabla f (x) = (\partial_{1} f (x), \dots, \partial_{n} f (x))^{T} .

When

f

D f (x) h = \nabla f (x) \cdot h .

Thus the Jacobian is the transpose of the gradient in standard Euclidean coordinates.

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