Product Rule

Xeerka isku-dhufashada (Product rule) waxa uu inoo sheegayaa habka loo xigo(differentiate) labo fansaar(function) oo isku dhufsan.
Product rule waxa uu inoo sheegayaa habka loo raadiyo derivative-ka labo function oo isku dhufsan.
(fg)' = f' . g + f . g'

Si aad u hesho xigsinta labo fansaar oo isku dhufsan( f \times g ):
– xig fansaarka hore(f’) oo ku dhufo fansaarka dambe oo aan xignayn(g), kaddibna waxa aad ku dartaa(+)
– xigsinta fansaarka dambe(g’) oo lagu dhuftay fansaarka hore oo aan xignayn(f).

Tusaale 1: If y= x^{2}(x+2) find y’
Furfuris (Solution):
fansaarka hore(f) waa x^{2} , fansaarka labaadna(g) waa x+2.
Raac Product Rule: y' = f' . g + f . g'
y= x^{2}(x+2)
y'= (x^{2})'(x+2) + x^{2} (x+2)' … xig
y'= (2x)(x+2) + x^{2} (1) …. isku dhufo
y'= 2x^{2}+4x + x^{2}  … isku dar 2x^{2} + x^{2}
y'= 3x^{2}+4x 

Tusaale 2: If y= (3x^{2}+1)(x^{2}+1) find y’
Furfuris (Solution):
fansaarka hore(f) waa (3x^{2}+1) , fansaarka labaadna(g) waa (x^{2}+1).
Raac Product Rule: y' = f' . g + f . g'
y= (3x^{2}+1)(x^{2}+1)
y'= (3x^{2}+1)' (x^{2}+1) + (3x^{2}+1)(x^{2}+1)' … xig
y'= (6x) (x^{2}+1) + (3x^{2}+1)(2x) …. isku dhufo
y'= (6x^{3}+6x) + (6x^{3}+2x) … isku dar 6x^{3} + 6x^{3} iyo 6x + 2x
y'= 12x^{3}+8x

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