Issolvi x^2/x^2+2x-3

$$\frac { x ^ { 2 } } { x ^ { 2 } + 2 x - 3 }$$

Iddifferenzja w.r.t. x

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

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.

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

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}.

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

Issimplifika.

$$\frac{\left(x^{2}+2x^{1}-3\right)\times 2x^{1}-x^{2}\left(2x^{1}+2x^{0}\right)}{\left(x^{2}+2x^{1}-3\right)^{2}}$$

Immultiplika x^{2}+2x^{1}-3 b'2x^{1}.

$$\frac{x^{2}\times 2x^{1}+2x^{1}\times 2x^{1}-3\times 2x^{1}-x^{2}\left(2x^{1}+2x^{0}\right)}{\left(x^{2}+2x^{1}-3\right)^{2}}$$

Immultiplika x^{2} b'2x^{1}+2x^{0}.

$$\frac{x^{2}\times 2x^{1}+2x^{1}\times 2x^{1}-3\times 2x^{1}-\left(x^{2}\times 2x^{1}+x^{2}\times 2x^{0}\right)}{\left(x^{2}+2x^{1}-3\right)^{2}}$$

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

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

Issimplifika.

$$\frac{2x^{3}+4x^{2}-6x^{1}-\left(2x^{3}+2x^{2}\right)}{\left(x^{2}+2x^{1}-3\right)^{2}}$$

Ikkombina termini simili.

$$\frac{2x^{2}-6x^{1}}{\left(x^{2}+2x^{1}-3\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{2x^{2}-6x}{\left(x^{2}+2x-3\right)^{2}}$$

Evalwa

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