Datrys -x^4/x^2+1

$$\frac { - x ^ { 4 } } { x ^ { 2 } + 1 }$$

Gwahaniaethu w.r.t. x

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

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.

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

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

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

Gwneud y symiau.

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

Ehangu gan ddefnyddio’r briodwedd ddosbarthol.

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

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

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

Gwneud y symiau.

$$\frac{-4x^{5}-4x^{3}-\left(-2x^{5}\right)}{\left(x^{2}+1\right)^{2}}$$

Cyfuno termau sydd yr un peth.

$$\frac{\left(-4-\left(-2\right)\right)x^{5}-4x^{3}}{\left(x^{2}+1\right)^{2}}$$

Tynnu -2 o -4.

$$\frac{-2x^{5}-4x^{3}}{\left(x^{2}+1\right)^{2}}$$

Ffactora allan 2x^{3}.

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

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

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

Enrhifo

$$-\frac{x^{4}}{x^{2}+1}$$