Exercise Solution 2.18
The Jacobian of f is given by
[s1]
We can solve this problem by valuing each of the four derivatives—analytically or using finite differences—individually. Solutions are:

The analytic solution is
[s2]
[s3]

The central approximation matches the analytic solution to the number of decimal places indicated.
[s4]
 The forward approximation is not as good:
[s5]
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