Usually when we speak of functions, we are talking about explicit functions of the form y = f(x). Sometimes we have instead an equation in x and y, for example, x + y + xy = sin(x + y), which may not be solvable for y. The solutions to this equation are a set of points {(x,y)} which implicitly define a relation between x and y which we will call an implicit function . Implicit functions are often not actually functions in the strict definition of the word, because they often have multiple y values for a single x value. They do have graphs and derivatives however. This worksheet explores implicit functions and implicit differentiation.