 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/discrete-mathematics-continuous-mathematics-and-probability/6/a/i/solution

Write

r = x - a

. The squared Euclidean norm is

r^{T} r

, whose gradient is

2 r

. The chain rule for the exponential function therefore gives the column gradient

\nabla f (x) = 2 e^{∥ x - a ∥^{2}} (x - a) .

The row derivative, if that convention is used for

df / d x

, is its transpose.

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