Issolvi x^2/x+1

$$\frac { x ^ { 2 } } { x + 1 }$$

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Għal kwalunkwe żewġ funzjonijiet differenzjabbli, id-derivattiv tal-kwozjent ta' żewġ funzjonijiet huwa d-denominatur immultiplikat bid-derivattiv tan-numeratur minus in-numeratur immultiplikat bid-derivattiv tad-denominatur, kollha diviżi bid-denominatur kwadrat.

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

Id-derivattiv ta' polynomial huwa s-somma tad-derivattivi tat-termini tiegħu. Id-derivattiv ta' kwalunkwe terminu kostanti huwa 0. Id-derivattiv ta' ax^{n} huwa nax^{n-1}.

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

Agħmel l-aritmetika.

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

Espandi bl-użu ta' propjetà distributtiva.

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

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom.

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

Agħmel l-aritmetika.

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

Ikkombina termini simili.

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

Naqqas 1 minn 2.

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

Iffattura 'l barra x.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

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

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

Għal kwalunkwe terminu t, t\times 1=t u 1t=t.

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

Evalwa

$$\frac{x^{2}}{x+1}$$