Editing Implicit function (section)

==== Example 2 ====
An example of an implicit function for which implicit differentiation is easier than using explicit differentiation is the function {{math|''y''(''x'')}} defined by the equation

:<math> x^4 + 2y^2 = 8 \,.</math>

To differentiate this explicitly with respect to {{mvar|x}}, one has first to get

:<math>y(x) = \pm\sqrt{\frac{8 - x^4}{2}} \,,</math>

and then differentiate this function. This creates two derivatives: one for {{math|''y'' ≥ 0}} and another for {{math|''y'' < 0}}.

It is substantially easier to implicitly differentiate the original equation:

:<math>4x^3 + 4y\frac{dy}{dx} = 0 \,,</math>

giving

:<math>\frac{dy}{dx} = \frac{-4x^3}{4y} = -\frac{x^3}{y} \,.</math>