Difference between revisions of "Product rule"

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==See also==
 
==See also==
 
* [[Chain rule]]
 
* [[Chain rule]]
 
{{Todo|Make this page "proper"}}
 

Latest revision as of 18:45, 28 August 2015

Definition

Given two functions f:RR and g:RR which are differentiable (at p) the composite function h:RR where h=fg has derivative:

  • dhdx|p=ddx[fg]|p=f(p)dgdx|p+g(p)dfdx|p
  • Phonetically first times derivative of second plus second times derivative of first

Example

  • 4x2ex
    • ddx[4x2ex]=4x2ddx[ex]+exddx[4x2]
      =4x2(1)ex+4exddx[x2]
      =4ex(ddx[x2]x2)
      =4ex(2xx2)
      =4xex(2x)

See also