Power Rule

    Power rule (Xeerka jibbaarka) waa mid ka mid ah xeerarka ugu adeegsiga badan Kalkulaska, waxa uu dhigayaa: 
   Xigsinta(Derivative)  x^{n} waa nx^{n-1}
         Si aad u hesho xigsinta jibbaar (Derivative-ka Power), horay kaga dhufo jibbaarka, kaddibna jibbaarka hal ka jar.

Tusaale 1: Waa maxay xigsinta x^{2} ?
Xigsinta x^{2} = 2x^{(2-1)} 
                    =
2x^{1}
                    = 2x

Tusaale 2: Find \frac{dy}{dx} of 2x^{4}
\frac{dy}{dx} 2x^{4} = 4\times2x^{(4-1)} 
             = 8x^{3}

Tusaale 3: Xig \frac{1}{x^{3}}
 Derivative-ka 2x^{4} = 4\times2x^{(4-1)} 
                                 = 8x^{3}

Tusaale 4: Waa maxay xigsinta \frac{1} {x^{3}} ?
Furfuris (Solution):
\frac{1} {x^{3}} Waxa aynu kor u wareejinaynaa hooseeyaha: x^{-3}

Xigsinta x^{-3} = -3x^{(-3-1)} 
                        =
-3x^{-4}
                        = 2x

Tusaale 5: what is the derivative of \frac{3} {4x^{2}} ?
Furfuris (Solution):
\frac{3} {4x^{2}} Waxa aynu u qori karnaa qaabkan: \frac{3}{4}x^{-2}
Jibbaarka horay kaga dhufo, isagana hal ka jar.

Xigsinta \frac{3}{4}x^{-2} = -2\times\frac{3}{4}x^{(-2-1)} 
                           =
\frac{-3}{2}x^{-3}
                    

Tusaale 6: Waa maxay xigsinta 2 ?
Furfuris (Solution):
2 Waxa aynu u qori karnaa: 2x^{0}
Xigsinta 2x^{0} = 0\times 2x^{(0-1)}
                    =
0\times 2x^{-1}
                    = 0
Haddaba xigsinta tiro sugan waa 0.
The derivative of a constant = 0.


Jadwalkan waxa uu soo koobayaa dulucda casharka:
f f^{'}x^{n}=nx^{(n-1)} f^{'}
x 1x^{(1-1)}=1x^{0} 1
x^{5} 5x^{(5-1)}=5x^{4} 5x^{4}
x^{-3} -3x^{(-3-1)}= -3x^{-4} -3x^{-4}
x^{-1} -1x^{(-1-1)}= -1x^{-2} -x^{-2}= \frac {-1} {x^{2}}