[doc] use DiffOpt to compute dydx in Nested problem tutorial

[odow]

Previously, we just ignored the contribution from dy/dx because it was too tedious to compute in a tutorial.

This is actually a good reason to add DiffOpt in the documentation.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.96%. Comparing base (6a4d22d) to head (27504cd).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #4248   +/-   ##
=======================================
  Coverage   99.96%   99.96%           
=======================================
  Files          43       43           
  Lines        6304     6304           
=======================================
  Hits         6302     6302           
  Misses          2        2           

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