PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (236)
Orphanage
Unclass'd (1)
Unproven (540)
Corrections (46)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Copyright
About
Owner confidence rating: Very high Entry average rating: No information on entry rating
[parent] proof of sum rule (Proof)


$\displaystyle \ensuremath{\frac{\ensuremath{\mathrm{d}}}{\ensuremath{\mathrm{d}x}}}\left[f(x)+g(x)\right]$ $\displaystyle =$ $\displaystyle \lim_{h\to0}\frac{f(x+h)+g(x+h)-f(x)-g(x)}{h}$  
  $\displaystyle =$ $\displaystyle \lim_{h\to0}\left[\frac{f(x+h)-f(x)}{h}+\frac{g(x+h)-g(x)}{h}\right]$  
  $\displaystyle =$ $\displaystyle f'(x) + g'(x)$  



"proof of sum rule" is owned by mathcam. [ full author list (2) | owner history (1) ]
(view preamble | get metadata)

View style:

See Also: derivative, fixed points of normal functions


This object's parent.
Log in to rate this entry.
(view current ratings)

There is 1 reference to this entry.

This is version 2 of proof of sum rule, born on 2002-02-24, modified 2004-03-22.
Object id is 2638, canonical name is ProofOfSumRule.
Accessed 5043 times total.

Classification:
AMS MSC: 26A24 (Real functions :: Functions of one variable :: Differentiation : general theory, generalized derivatives, mean-value theorems)
Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add example | add (any)