sum rule

The sum rule states that

$$\frac{\mathrm{d}}{\mathrm{d}x}\left[f(x)+g(x)\right]=f^{\prime }(x)+g^{\prime }(x)$$

Proof

See the proof of the sum rule (http://planetmath.org/ProofOfSumRule).

Examples

${\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}(x+1)$ $=$ ${\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}x+{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}1=1$

${\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}(x^2-3x+2)$ $=$ ${\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}{x}^2+{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}(-3x)+{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}(2)=2x-3$

${\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}(\sin x+\cos x)$ $=$ ${\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}\sin x+{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}\cos x=\cos x-\sin x$

Title	sum rule
Canonical name	SumRule
Date of creation	2013-03-22 12:28:09
Last modified on	2013-03-22 12:28:09
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	8
Author	mathcam (2727)
Entry type	Theorem
Classification	msc 26A24
Related topic	Derivative
Related topic	ProductRule
Related topic	FixedPointsOfNormalFunctions