hey can someone explain to me the relationship between the chain rule and implicit differentiation? It would be very much appreicated, thanks

The chain rule is utilized whenever you have a function within a function such as cos^2 x or (5x+1)^1/2. Implicit differentiation is used to find dy/dx of a function such as x^2 + y^2 = 1. Some functions require that you use the chain rule when you are trying to find their derivative through implicit differentiation.