View source for Product rule

==Definition==
Given two functions {{M|f:\mathbb{R}\rightarrow\mathbb{R} }} and {{M|g:\mathbb{R}\rightarrow\mathbb{R} }} which are differentiable (at {{M|p}}) the composite function {{M|h:\mathbb{R}\rightarrow\mathbb{R} }} where {{M|1=h=fg}} has derivative:

* <math>\frac{dh}{dx}\Bigg|_p=\frac{d}{dx}[fg]\Bigg|_p=f(p)\frac{dg}{dx}\Bigg|_p+g(p)\frac{df}{dx}\Bigg|_p</math>
* Phone me up ma bree ''first times derivative of second plus second times derivative of first''

==Example==
* <math>4x^2e^{-x}</math>
** <math>\frac{d}{dx}\Big[4x^2e^{-x}\Big]=4x^2\frac{d}{dx}\Big[e^{-x}\Big]+e^{-x}\frac{d}{dx}\Big[4x^2\Big]</math>
**: <math>=4x^2(-1)e^{-x}+4e^{-x}\frac{d}{dx}\Big[x^2\Big]</math>
**: <math>=4e^{-x}\Big(\frac{d}{dx}\Big[x^2\Big]-x^2\Big)</math>
**: <math>=4e^{-x}\big(2x-x^2\big)</math>
**: <math>=4xe^{-x}(2-x)</math>

==See also==
* [[Chain rule]]
* [[kernal of corn]]

{{Todo|Make this page "proper"}}