The curve defined by the equation {{MATH_76}} is not a graph of a function. If we solve for {{MATH_77}}, we obtain two solutions: {{MATH_78}} and {{MATH_79}}. Therefore, we can say that any point {{MATH_80}} on the curve lies on the graph of some function {{MATH_81}}. Starting with {{MATH_82}} we differentiate both sides of the equation with respect to {{MATH_83}} to obtain {{MATH_84}} Applying the sum rule we see {{MATH_85}} Let's examine each of these terms in turn. To start {{MATH_86}} On the other hand, {{MATH_87}} is somewhat different. Here we assume that {{MATH_88}} for some function {{MATH_89}}, defined on some open interval (this is true for all points {{MATH_90}}). Hence, by the chain rule {{ENV_91}} Putting this together, we are left with the equation {{MATH_92}} At this point, we solve for {{MATH_93}}. Write {{ENV_94}} Remark: Notice that the derivative {{MATH_95}} is expressed in terms of both variables {{MATH_96}} and {{MATH_97}}. This should not come as a surprise. If you think about it, the function and its derivative are not determined solely by the value of {{MATH_98}}. Recall what happens if {{MATH_99}}.