Computing derivatives of implicit functions
Channel: OpenMDAO
Date: 01/02/2023

Computing derivatives of implicit functions can seem quite confusing at first, but it is not markedly harder than computing derivatives of explicit functions. Instead of getting d_outputs/d_inputs, you simply need to get d_residuals/d_inputs and d_residuals/d_outputs.

0:00 - Intro and context
1:15 - We need derivatives of the residual functions
3:02 - Explained example of getting derivatives
6:58 - Conclusion

Accompanying course page: https://openmdao.github.io/PracticalMDO/Notebooks/Differentiation/computing_derivs_of_implicit.html

Section 6.7-6.9 in Engineering Design Optimization by Martins and Ning at https://mdobook.github.io/