Past exam of the Probability, statistics and options II course of the University of Oxford / 2011 / F / F2 / a / iii

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- Solution iii

Solution

The chain rule at the specified point is

D (f \circ g) (x) = D f (g (x)) \circ D g (x) .

In standard coordinates this becomes

J_{f \circ g} (x) = J_{f} (g (x)) J_{g} (x) .

The matrix dimensions are respectively

k \times n

,

k \times m

, and

m \times n

, matching the composition of the two linear derivative maps.

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