 Solution

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

 New to topics? Read the docs here!