Datrys x^199/x^200+100

$$\frac { x ^ { 199 } } { x ^ { 200 } + 100 }$$

Gwahaniaethu w.r.t. x

$$\frac{x^{198}\left(19900-x^{200}\right)}{\left(x^{200}+100\right)^{2}}$$

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.

$$\frac{\left(x^{200}+100\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{199})-x^{199}\frac{\mathrm{d}}{\mathrm{d}x}(x^{200}+100)}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{\left(x^{200}+100\right)\times 199x^{199-1}-x^{199}\times 200x^{200-1}}{\left(x^{200}+100\right)^{2}}$$

Gwneud y symiau.

$$\frac{\left(x^{200}+100\right)\times 199x^{198}-x^{199}\times 200x^{199}}{\left(x^{200}+100\right)^{2}}$$

Ehangu gan ddefnyddio’r briodwedd ddosbarthol.

$$\frac{x^{200}\times 199x^{198}+100\times 199x^{198}-x^{199}\times 200x^{199}}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{199x^{200+198}+100\times 199x^{198}-200x^{199+199}}{\left(x^{200}+100\right)^{2}}$$

Gwneud y symiau.

$$\frac{199x^{398}+19900x^{198}-200x^{398}}{\left(x^{200}+100\right)^{2}}$$

Cyfuno termau sydd yr un peth.

$$\frac{\left(199-200\right)x^{398}+19900x^{198}}{\left(x^{200}+100\right)^{2}}$$

Tynnu 200 o 199.

$$\frac{-x^{398}+19900x^{198}}{\left(x^{200}+100\right)^{2}}$$

Ffactora allan x^{198}.

$$\frac{x^{198}\left(-x^{200}+19900x^{0}\right)}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{x^{198}\left(-x^{200}+19900\times 1\right)}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{x^{198}\left(-x^{200}+19900\right)}{\left(x^{200}+100\right)^{2}}$$

Enrhifo

$$\frac{x^{199}}{x^{200}+100}$$