The functions we've been dealing with so far have been defined {{CMD_18}}explicitly{{CMD_19}} in terms of the independent variable. For example: {{MATH_20}} However, this is not always necessary or even possible to do. Sometimes we choose to or we have to define a function {{CMD_21}}implicitly {{CMD_22}}. In this case, the dependent variable is not stated explicitly in terms of an independent variable. Some examples are: {{MATH_23}} Your inclination might be simply to solve each of these equations for {{MATH_24}} and go merrily on your way. However, this can be difficult or even impossible to do. {{COMMENT_25}} {{COMMENT_26}} Since we are often faced with a problem of computing derivatives of such functions, we need a method that will enable us to compute derivatives of implicitly defined functions. {{COMMENT_27}} {{COMMENT_28}} We'll start with a basic example. {{CMD_29}} Consider the curve (a circle) defined by: {{MATH_30}} {{CMD_31}}