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# Implicit derivatives

Implicit derivatives are derivative of functions that are not given in $y=ax^n$.... form.

For example:

$y=x^2+5$
$y'=2x$

If we do not have $y=ax^n$....

$y^2-x=25$
$2yy'-1=0$
$2yy'=1$
$y'=\frac{1}{2y}$ is the derivative

## Example in different notation

$x = 6y^2 + 5x^4 - y^3$

$1 = 12y \frac{dy}{dx} + 20x^3 - 3y^2 \frac{dy}{dx}$

$1 - 20x^3 = \frac{dy}{dx}(12y - 3y^2)$

$\therefore\ \frac{dy}{dx} = \frac{1 - 20x^3}{12y - 3y^2}$