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.
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}} |