kidzsearch.com > wiki   Explore:web images videos games  

Implicit derivatives




KidzSearch Safe Wikipedia for Kids.
Jump to: navigation, search


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

For example:

[math]y=x^2+5[/math]
[math]y'=2x[/math]

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

[math]y^2-x=25[/math]
[math]2yy'-1=0[/math]
[math]2yy'=1[/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]