proof of sum rule

${\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}\left[f(x)+g(x)\right]$ $=$ $\underset{h\to 0}{lim}{\displaystyle \frac{f(x+h)+g(x+h)-f(x)-g(x)}{h}}$

$=$ $\underset{h\to 0}{lim}\left[{\displaystyle \frac{f(x+h)-f(x)}{h}}+{\displaystyle \frac{g(x+h)-g(x)}{h}}\right]$

$=$ $f^{\prime }(x)+g^{\prime }(x)$

Title	proof of sum rule
Canonical name	ProofOfSumRule
Date of creation	2013-03-22 12:28:13
Last modified on	2013-03-22 12:28:13
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	5
Author	mathcam (2727)
Entry type	Proof
Classification	msc 26A24
Related topic	Derivative
Related topic	FixedPointsOfNormalFunctions