Issolvi n^2/n+1

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

Iddifferenzja w.r.t. n

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

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.

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

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}.

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

Agħmel l-aritmetika.

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

Espandi bl-użu ta' propjetà distributtiva.

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

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

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

Agħmel l-aritmetika.

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

Ikkombina termini simili.

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

Naqqas 1 minn 2.

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

Iffattura 'l barra n.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

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

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

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

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

Evalwa

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