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Calculus: Concepts and Methods by Joan Davies, Ken Binmore

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Eight

Implicit functions

The implicit function theorem is very easy to apply in practice provided that the material on vector derivatives given in Chapter 5 has been properly assimilated. We are therefore able to deal with it quite quickly in this chapter. Some understanding of §8.2 is necessary for the conclusion of the implicit function theorem to be meaningful but too much time should not be spent on this section; especially in respect of the theoretical discussion at the end of the section which links the proof of the implicit function theorem with the discussion of local inverses given in the previous chapter.

8.1 Implicit differentiation ...

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