Issolvi x^2/x^2+1

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

Iddifferenzja w.r.t. x

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

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.

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

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}.

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

Agħmel l-aritmetika.

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

Espandi bl-użu ta' propjetà distributtiva.

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

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

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

Agħmel l-aritmetika.

$$\frac{2x^{3}+2x^{1}-2x^{3}}{\left(x^{2}+1\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(2-2\right)x^{3}+2x^{1}}{\left(x^{2}+1\right)^{2}}$$

Naqqas 2 minn 2.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

Evalwa

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