Issolvi f(y)=x^2/2x-1

$$f ( y ) = \frac { x ^ { 2 } } { 2 x - 1 }$$

Iddifferenzja w.r.t. x

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

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.

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

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}.

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

Agħmel l-aritmetika.

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

Espandi bl-użu ta' propjetà distributtiva.

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

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

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

Agħmel l-aritmetika.

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

Ikkombina termini simili.

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

Naqqas 2 minn 4.

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

Iffattura 'l barra 2x.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

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

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

Evalwa

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