Editing Implicit function (section)

==== Example 1 ====
Consider

:<math>y + x + 5 = 0 \,.</math>

This equation is easy to solve for {{mvar|y}}, giving

:<math>y = -x - 5 \,,</math>

where the right side is the explicit form of the function {{math|''y''(''x'')}}. Differentiation then gives {{math|1={{sfrac|''dy''|''dx''}} = −1}}.

Alternatively, one can totally differentiate the original equation:

:<math>\begin{align}
\frac{dy}{dx} + \frac{dx}{dx} + \frac{d}{dx}(5) &= 0 \, ; \\[6px]
\frac{dy}{dx} + 1 + 0 &= 0 \,.
\end{align}</math>

Solving for {{math|{{sfrac|''dy''|''dx''}}}} gives

:<math>\frac{dy}{dx} = -1 \,,</math>

the same answer as obtained previously.