Issolvi 2x/(x+30)

$$2 x / ( x + 30 )$$

Iddifferenzja w.r.t. x

$$\frac{60}{\left(x+30\right)^{2}}$$

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.

$$\frac{\left(x^{1}+30\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1})-2x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+30)}{\left(x^{1}+30\right)^{2}}$$

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}.

$$\frac{\left(x^{1}+30\right)\times 2x^{1-1}-2x^{1}x^{1-1}}{\left(x^{1}+30\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{\left(x^{1}+30\right)\times 2x^{0}-2x^{1}x^{0}}{\left(x^{1}+30\right)^{2}}$$

Espandi bl-użu ta' propjetà distributtiva.

$$\frac{x^{1}\times 2x^{0}+30\times 2x^{0}-2x^{1}x^{0}}{\left(x^{1}+30\right)^{2}}$$

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

$$\frac{2x^{1}+30\times 2x^{0}-2x^{1}}{\left(x^{1}+30\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{2x^{1}+60x^{0}-2x^{1}}{\left(x^{1}+30\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(2-2\right)x^{1}+60x^{0}}{\left(x^{1}+30\right)^{2}}$$

Naqqas 2 minn 2.

$$\frac{60x^{0}}{\left(x^{1}+30\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{60x^{0}}{\left(x+30\right)^{2}}$$

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

$$\frac{60\times 1}{\left(x+30\right)^{2}}$$

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

$$\frac{60}{\left(x+30\right)^{2}}$$

Evalwa

$$\frac{2x}{x+30}$$