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Implicit derivatives

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Implicit derivatives are derivative of functions that are not given in [math]y=ax^n[/math].... form.

For example:


If we do not have [math]y=ax^n[/math]....

[math]y'=\frac{1}{2y}[/math] is the derivative

Example in different notation

[math]x = 6y^2 + 5x^4 - y^3[/math]

[math]1 = 12y \frac{dy}{dx} + 20x^3 - 3y^2 \frac{dy}{dx}[/math]

[math]1 - 20x^3 = \frac{dy}{dx}(12y - 3y^2)[/math]

[math]\therefore\ \frac{dy}{dx} = \frac{1 - 20x^3}{12y - 3y^2}[/math]