I’ve been thinking about implicit differentiation with my colleagues
recently. How do we teach it (at high school level), and what
subtleties are involved? It started by trying to understand what we
mean by the equation
Some questions raised by this include:
(a) What does this equation mean?
(b) How can we explain this to students and also why it is true?
(c) Where would this result be useful to them (besides in artificial
In this post, I will offer some thoughts on (a) and (b), but I’m still
fairly stuck on (c).