Réitigh d/dxleft(1/x(x-y)right)

$$\frac{d}{d x } \left( \frac{ 1 }{ x(x-y) } \right)$$

Luacháil

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

Céimeanna ag Baint Úsáid as an Riail Slabhra

Úsáid an t-airí dáileach chun x a mhéadú faoi x-y.

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

Más F comhshuíomh dhá fheidhm indifreáilte f\left(u\right) agus u=g\left(x\right), is é sin, más F\left(x\right)=f\left(g\left(x\right)\right), mar sin is ionann díorthach F agus díorthach f maidir le u méadaithe faoi dhíorthach g maidir le x, is é sin, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

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}.

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

Simpligh.

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

Do théarma ar bith t, t^{1}=t.

$$\left(x^{2}+\left(-y\right)x\right)^{-2}\left(-2x+yx^{0}\right)$$

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

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

Do théarma ar bith t, t\times 1=t agus 1t=t.

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

Difreálaigh w.r.t. x

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