# 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]