Issolvi x/65+x

$$\frac{ x }{ 65+x }$$

Iddifferenzja w.r.t. x

$$\frac{65}{\left(x+65\right)^{2}}$$

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.

$$\frac{\left(x^{1}+65\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+65)}{\left(x^{1}+65\right)^{2}}$$

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}.

$$\frac{\left(x^{1}+65\right)x^{1-1}-x^{1}x^{1-1}}{\left(x^{1}+65\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{\left(x^{1}+65\right)x^{0}-x^{1}x^{0}}{\left(x^{1}+65\right)^{2}}$$

Espandi bl-użu ta' propjetà distributtiva.

$$\frac{x^{1}x^{0}+65x^{0}-x^{1}x^{0}}{\left(x^{1}+65\right)^{2}}$$

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

$$\frac{x^{1}+65x^{0}-x^{1}}{\left(x^{1}+65\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(1-1\right)x^{1}+65x^{0}}{\left(x^{1}+65\right)^{2}}$$

Naqqas 1 minn 1.

$$\frac{65x^{0}}{\left(x^{1}+65\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{65x^{0}}{\left(x+65\right)^{2}}$$

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

$$\frac{65\times 1}{\left(x+65\right)^{2}}$$

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

$$\frac{65}{\left(x+65\right)^{2}}$$

Evalwa

$$\frac{x}{x+65}$$