Patakarang adisyon at subtraksiyon

Ang Patakarang adisyon at subtraksiyon(Addition and Subtraction Rules) ay isang paraan upang mahanap ang deribatibo ng isang punsiyon.

$\frac{d}{dx}[f(x)\pm g(x)]=\frac{d}{dx}[f(x)]\pm \frac{d}{dx}[g(x)]$

Patunay

Mula sa depinisyon ng deribatibo:

$\underset{\mathrm{\Delta }x\to 0}{\lim }\left[\frac{[f(x+\mathrm{\Delta }x)\pm g(x+\mathrm{\Delta }x)]-[f(x)\pm g(x)]}{\mathrm{\Delta }x}\right]$

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

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

Sa pamamagitan ng kahulugan, ang huling termino ay $\frac{d}{dx}[f(x)]\pm \frac{d}{dx}[g(x)]$

Halimbawa

$\frac{d}{dx}[3x^2+5x]$	= $\frac{d}{dx}[3x^2+5x]$
	= $\frac{d}{dx}\left[3x^2\right]+\frac{d}{dx}\left[5x\right]$
	= $6x+\frac{d}{dx}\left[5x\right]$
	= $6x+5$