Because he's for some reason differentiating with respect to y. You're right, "implicit differentiation" is nothing more than just differentiating both sides o

Because he's for some reason differentiating with respect to y. You're right, "implicit differentiation" is nothing more than just differentiating both sides of an equation. Pedagogically, it is a bit of a step up from "here's a single expression that denotes a function, differentiate it". You have to recognize that differentiation is an operation on functions, and then you have to realize that something like "9=y^2+x^2" really means "9=y(x)^2 + x^2 for all values of x" (or equivalently as an equation of functions, the constant function 9 = y^2 + id^2) and that it's valid to apply the differentiation operator to both sides. Many calculus courses probably gloss over subtleties like this or expect students to be able to "intuitively" grasp them (and many very well may), but I can see it leading to confusion.