power rule

The power ruleMathworldPlanetmathPlanetmath states that


This rule, when combined with the chain ruleMathworldPlanetmath, product ruleMathworldPlanetmath, and sum ruleMathworldPlanetmath, makes calculating many derivatives far more tractable. This rule can be derived by repeated application of the product rule. See the proof of the power rule (http://planetmath.org/ProofOfPowerRule).

Repeated use of the above formula gives


for i,k.


ddxx0 = 0x=0=ddx1
ddxx1 = 1x0=1=ddxx
ddxx2 = 2x
ddxx3 = 3x2
ddxx = ddxx1/2=12x-1/2=12x
ddx2xe = 2exe-1
Title power rule
Canonical name PowerRule
Date of creation 2013-03-22 12:28:03
Last modified on 2013-03-22 12:28:03
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 7
Author mathcam (2727)
Entry type Theorem
Classification msc 26A03
Related topic ProductRule
Related topic Derivation
Related topic Derivative