Réitigh f(x)=x/x^2-6x-16

$$f ( x ) = \frac { x } { x ^ { 2 } - 6 x - 16 }$$

Difreálaigh w.r.t. x

$$-\frac{x^{2}+16}{\left(\left(x-8\right)\left(x+2\right)\right)^{2}}$$

Céimeanna ag Baint Úsáid as Riail na nDíorthach don Líon

Do dhá fheidhm indifreáilte ar bith, is ionann díorthach líon an dá fheidhme agus an t-ainmneoir méadaithe faoi dhíorthach an uimhreora lúide an t-uimhreoir méadaithe faoi dhíorthach an ainmneora, agus iad ar fad roinnte faoin ainmneoir cearnaithe.

$$\frac{\left(x^{2}-6x^{1}-16\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-6x^{1}-16)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Is ionann díorthach iltéarmaigh agus suim dhíorthaigh a théarmaí. Is ionann díorthach téarma thairisigh agus 0. Is ionann díorthach ax^{n} agus nax^{n-1}.

$$\frac{\left(x^{2}-6x^{1}-16\right)x^{1-1}-x^{1}\left(2x^{2-1}-6x^{1-1}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}-6x^{1}-16\right)x^{0}-x^{1}\left(2x^{1}-6x^{0}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Méadaigh x^{2}-6x^{1}-16 faoi x^{0}.

$$\frac{x^{2}x^{0}-6x^{1}x^{0}-16x^{0}-x^{1}\left(2x^{1}-6x^{0}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Méadaigh x^{1} faoi 2x^{1}-6x^{0}.

$$\frac{x^{2}x^{0}-6x^{1}x^{0}-16x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\left(-6\right)x^{0}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Chun cumhachtaí an bhoinn chéanna a mhéadú, suimigh a n-easpónaint.

$$\frac{x^{2}-6x^{1}-16x^{0}-\left(2x^{1+1}-6x^{1}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Simpligh.

$$\frac{x^{2}-6x^{1}-16x^{0}-\left(2x^{2}-6x^{1}\right)}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{-x^{2}-16x^{0}}{\left(x^{2}-6x^{1}-16\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{-x^{2}-16x^{0}}{\left(x^{2}-6x-16\right)^{2}}$$

Do théarma ar bith t ach amháin 0, t^{0}=1.

$$\frac{-x^{2}-16}{\left(x^{2}-6x-16\right)^{2}}$$

Luacháil

$$\frac{x}{\left(x-8\right)\left(x+2\right)}$$