Datrys f(t)=2t/1+2t^2

$$f ( t ) = \frac { 2 t } { 1 + 2 t ^ { 2 } }$$

Gwahaniaethu w.r.t. t

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

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.

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

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

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

Gwneud y symiau.

$$\frac{\left(2t^{2}+1\right)\times 2t^{0}-2t^{1}\times 4t^{1}}{\left(2t^{2}+1\right)^{2}}$$

Ehangu gan ddefnyddio’r briodwedd ddosbarthol.

$$\frac{2t^{2}\times 2t^{0}+2t^{0}-2t^{1}\times 4t^{1}}{\left(2t^{2}+1\right)^{2}}$$

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

$$\frac{2\times 2t^{2}+2t^{0}-2\times 4t^{1+1}}{\left(2t^{2}+1\right)^{2}}$$

Gwneud y symiau.

$$\frac{4t^{2}+2t^{0}-8t^{2}}{\left(2t^{2}+1\right)^{2}}$$

Cyfuno termau sydd yr un peth.

$$\frac{\left(4-8\right)t^{2}+2t^{0}}{\left(2t^{2}+1\right)^{2}}$$

Tynnu 8 o 4.

$$\frac{-4t^{2}+2t^{0}}{\left(2t^{2}+1\right)^{2}}$$

Ffactora allan 2.

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

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

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

Enrhifo

$$\frac{2t}{2t^{2}+1}$$