Datrys x^4/6x+12

$$\frac{ { x }^{ 4 } }{ 6x+12 }$$

Gwahaniaethu w.r.t. x

$$\frac{\left(3x+8\right)x^{3}}{6\left(x+2\right)^{2}}$$

Camau gan Ddefnyddio Rheol Deilliadol ar gyfer Cyniferydd

Ar gyfer unrhyw ddau ffwythiant y mae modd eu gwahaniaethu, deilliad cyniferydd dau ffwythiant yw’r enwadur wedi’i luosi â deilliad yr enwadur wedi’i dynnu o’r rhifiadur wedi’i luosi â deilliad yr enwadur, y cwbl wedi’i rannu â’r enwadur wedi'i sgwario.

$$\frac{\left(6x^{1}+12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{4})-x^{4}\frac{\mathrm{d}}{\mathrm{d}x}(6x^{1}+12)}{\left(6x^{1}+12\right)^{2}}$$

Deilliad polynomaial yw swm deilliadau ei dermau. Deilliad term cyson yw 0. Y deilliad o ax^{n} yw nax^{n-1}.

$$\frac{\left(6x^{1}+12\right)\times 4x^{4-1}-x^{4}\times 6x^{1-1}}{\left(6x^{1}+12\right)^{2}}$$

Gwneud y symiau.

$$\frac{\left(6x^{1}+12\right)\times 4x^{3}-x^{4}\times 6x^{0}}{\left(6x^{1}+12\right)^{2}}$$

Ehangu gan ddefnyddio’r briodwedd ddosbarthol.

$$\frac{6x^{1}\times 4x^{3}+12\times 4x^{3}-x^{4}\times 6x^{0}}{\left(6x^{1}+12\right)^{2}}$$

I luosi pwerau sy’n rhannu’r un sail, ychwanegwch eu hesbonyddion.

$$\frac{6\times 4x^{1+3}+12\times 4x^{3}-6x^{4}}{\left(6x^{1}+12\right)^{2}}$$

Gwneud y symiau.

$$\frac{24x^{4}+48x^{3}-6x^{4}}{\left(6x^{1}+12\right)^{2}}$$

Cyfuno termau sydd yr un peth.

$$\frac{\left(24-6\right)x^{4}+48x^{3}}{\left(6x^{1}+12\right)^{2}}$$

Tynnu 6 o 24.

$$\frac{18x^{4}+48x^{3}}{\left(6x^{1}+12\right)^{2}}$$

Ffactora allan 6x^{3}.

$$\frac{6x^{3}\left(3x^{1}+8x^{0}\right)}{\left(6x^{1}+12\right)^{2}}$$

Ar gyfer unrhyw derm t, t^{1}=t.

$$\frac{6x^{3}\left(3x+8x^{0}\right)}{\left(6x+12\right)^{2}}$$

Ar gyfer unrhyw derm t ac eithrio 0, t^{0}=1.

$$\frac{6x^{3}\left(3x+8\times 1\right)}{\left(6x+12\right)^{2}}$$

Ar gyfer unrhyw derm t, t\times 1=t a 1t=t.

$$\frac{6x^{3}\left(3x+8\right)}{\left(6x+12\right)^{2}}$$

Enrhifo

$$\frac{x^{4}}{6\left(x+2\right)}$$