This document summarizes a calculus lesson on implicit differentiation. The lesson began with examples of implied relationships in pictures and led into a discussion of implicit functions hidden within explicit functions. The class then learned how to take the derivative of an implicit function using the example of finding the derivative of any point on a circle. The process involves rewriting the equation in terms of y, applying the chain rule, and solving for the derivative of y. The lesson concluded by emphasizing that the derivative is zero when the numerator is zero, indicating a horizontal tangent line, and when the denominator is zero, indicating a vertical tangent line.