Datrys v/v+1+3/v-1-6/v^2-1

$$\frac { v } { v + 1 } + \frac { 3 } { v - 1 } - \frac { 6 } { v ^ { 2 } - 1 }$$

Enrhifo

$$\frac{v+3}{v+1}$$

Camau Ateb Byr

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluosrif lleiaf cyffredin v+1 a v-1 yw \left(v-1\right)\left(v+1\right). Lluoswch \frac{v}{v+1} â \frac{v-1}{v-1}. Lluoswch \frac{3}{v-1} â \frac{v+1}{v+1}.

$$\frac{v\left(v-1\right)}{\left(v-1\right)\left(v+1\right)}+\frac{3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1}$$

Gan fod gan \frac{v\left(v-1\right)}{\left(v-1\right)\left(v+1\right)} a \frac{3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

$$\frac{v\left(v-1\right)+3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1}$$

Gwnewch y gwaith lluosi yn v\left(v-1\right)+3\left(v+1\right).

$$\frac{v^{2}-v+3v+3}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1}$$

Cyfuno termau tebyg yn v^{2}-v+3v+3.

$$\frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1}$$

Ffactora v^{2}-1.

$$\frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)}-\frac{6}{\left(v-1\right)\left(v+1\right)}$$

Gan fod gan \frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)} a \frac{6}{\left(v-1\right)\left(v+1\right)} yr un dynodydd, tynnwch nhw drwy dynnu eu rhifiaduron.

$$\frac{v^{2}+2v+3-6}{\left(v-1\right)\left(v+1\right)}$$

Cyfuno termau tebyg yn v^{2}+2v+3-6.

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

Dylech ffactoreiddio'r mynegiadau sydd heb eu ffactoreiddio eisoes yn \frac{v^{2}+2v-3}{\left(v-1\right)\left(v+1\right)}.

$$\frac{\left(v-1\right)\left(v+3\right)}{\left(v-1\right)\left(v+1\right)}$$

Canslo v-1 yn y rhifiadur a'r enwadur.

$$\frac{v+3}{v+1}$$

Gwahaniaethu w.r.t. v

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

Camau gan Ddefnyddio Rheol Deilliadol ar gyfer Cyniferydd

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluosrif lleiaf cyffredin v+1 a v-1 yw \left(v-1\right)\left(v+1\right). Lluoswch \frac{v}{v+1} â \frac{v-1}{v-1}. Lluoswch \frac{3}{v-1} â \frac{v+1}{v+1}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v\left(v-1\right)}{\left(v-1\right)\left(v+1\right)}+\frac{3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1})$$

Gan fod gan \frac{v\left(v-1\right)}{\left(v-1\right)\left(v+1\right)} a \frac{3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v\left(v-1\right)+3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1})$$

Gwnewch y gwaith lluosi yn v\left(v-1\right)+3\left(v+1\right).

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}-v+3v+3}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1})$$

Cyfuno termau tebyg yn v^{2}-v+3v+3.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)}-\frac{6}{v^{2}-1})$$

Ffactora v^{2}-1.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)}-\frac{6}{\left(v-1\right)\left(v+1\right)})$$

Gan fod gan \frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)} a \frac{6}{\left(v-1\right)\left(v+1\right)} yr un dynodydd, tynnwch nhw drwy dynnu eu rhifiaduron.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}+2v+3-6}{\left(v-1\right)\left(v+1\right)})$$

Cyfuno termau tebyg yn v^{2}+2v+3-6.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}+2v-3}{\left(v-1\right)\left(v+1\right)})$$

Dylech ffactoreiddio'r mynegiadau sydd heb eu ffactoreiddio eisoes yn \frac{v^{2}+2v-3}{\left(v-1\right)\left(v+1\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{\left(v-1\right)\left(v+3\right)}{\left(v-1\right)\left(v+1\right)})$$

Canslo v-1 yn y rhifiadur a'r enwadur.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v+3}{v+1})$$

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.

$$\frac{\left(v^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}v}(v^{1}+3)-\left(v^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}v}(v^{1}+1)}{\left(v^{1}+1\right)^{2}}$$

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

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

Gwneud y symiau.

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

Ehangu gan ddefnyddio’r briodwedd ddosbarthol.

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

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

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

Tynnu’r cromfachau diangen.

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

Cyfuno termau sydd yr un peth.

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

Tynnwch 1 o 1 a 3 o 1.

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

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

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

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

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