 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2005/f/1/iii/solution

The

j

th column of the matrix of

D f (a)

in the standard bases is

D f (a) e_{j}

. Its

i

th component is

\partial f_{i} / \partial x_{j} (a)

, found by taking increments

t e_{j}

. Thus the matrix of the total derivative is the Jacobian matrix, with entry

(i, j)

equal to

\partial f_{i} / \partial x_{j} (a)

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