Issolvi (x-1-sqrt{2})(x-1+sqrt{2})

$$( x - 1 - \sqrt { 2 } ) ( x - 1 + \sqrt { 2 } )$$

Evalwa

$$x^{2}-2x-1$$

Passi tas-Soluzzjonijiet

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' x-1-\sqrt{2} b'kull terminu ta' x-1+\sqrt{2}.

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

Ikkombina -x u -x biex tikseb -2x.

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

Ikkombina x\sqrt{2} u -\sqrt{2}x biex tikseb 0.

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

Ikkombina -\sqrt{2} u \sqrt{2} biex tikseb 0.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

$$x^{2}-2x+1-2$$

Naqqas 2 minn 1 biex tikseb -1.

$$x^{2}-2x-1$$

Iddifferenzja w.r.t. x

$$2\left(x-1\right)$$

Passi għall-Użu ta' Regola Derivattiva għal Somma

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' x-1-\sqrt{2} b'kull terminu ta' x-1+\sqrt{2}.

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

Ikkombina -x u -x biex tikseb -2x.

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

Ikkombina x\sqrt{2} u -\sqrt{2}x biex tikseb 0.

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

Ikkombina -\sqrt{2} u \sqrt{2} biex tikseb 0.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Naqqas 2 minn 1 biex tikseb -1.

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

Id-derivattiva ta’ polynomial hija s-somma tad-derivattivi tat-termini tagħha. Id-derivattiva ta’ terminu kostanti hija 0. Id-derivattiva ta’ ax^{n} hijanax^{n-1}.

$$2x^{2-1}-2x^{1-1}$$

Naqqas 1 minn 2.

$$2x^{1}-2x^{1-1}$$

Naqqas 1 minn 1.

$$2x^{1}-2x^{0}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$2x-2x^{0}$$

Għal kwalunkwe terminu t ħlief 0, t^{0}=1.

$$2x-2$$