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Implicit derivatives facts for kids

Kids Encyclopedia Facts


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}

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