Datrys d/dxx^2(2+x)/x^2-x

$$\frac { d } { d x } \frac { x ^ { 2 } ( 2 + x ) } { x ^ { 2 } - x }$$

Enrhifo

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

Camau gan Ddefnyddio Rheol Deilliadol ar gyfer Cyniferydd

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

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

Canslo x yn y rhifiadur a'r enwadur.

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

Defnyddio’r briodwedd ddosbarthu i luosi x â x+2.

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

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.

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

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

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

Symleiddio.

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

Lluoswch x^{1}-1 â 2x^{1}+2x^{0}.

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

Lluoswch x^{2}+2x^{1} â x^{0}.

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

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

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

Symleiddio.

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

Cyfuno termau sydd yr un peth.

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

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

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

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

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

Gwahaniaethu w.r.t. x

$$\frac{6}{\left(x-1\right)^{3}}$$