Difference between revisions of "Product rule"
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==Definition== | ==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: | 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> | * <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== | ==Example== | ||
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==See also== | ==See also== | ||
* [[Chain rule]] | * [[Chain rule]] | ||
| + | * [[kernal of corn]] | ||
{{Todo|Make this page "proper"}} | {{Todo|Make this page "proper"}} | ||
Revision as of 07:42, 23 August 2015
Definition
Given two functions f:R→R and g:R→R which are differentiable (at p) the composite function h:R→R where h=fg has derivative:
- dhdx|p=ddx[fg]|p=f(p)dgdx|p+g(p)dfdx|p
- Phone me up ma bree first times derivative of second plus second times derivative of first
Example
- 4x2e−x
- ddx[4x2e−x]=4x2ddx[e−x]+e−xddx[4x2]
- =4x2(−1)e−x+4e−xddx[x2]
- =4e−x(ddx[x2]−x2)
- =4e−x(2x−x2)
- =4xe−x(2−x)
- ddx[4x2e−x]=4x2ddx[e−x]+e−xddx[4x2]
See also
TODO: Make this page "proper"
