Issolvi d/dx(x/x^2+1)

$$\frac { d } { d x } ( \frac { x } { x ^ { 2 } + 1 } )$$

Evalwa

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

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.

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

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}.

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

Agħmel l-aritmetika.

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

Espandi bl-użu ta' propjetà distributtiva.

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

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

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

Agħmel l-aritmetika.

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

Ikkombina termini simili.

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

Naqqas 2 minn 1.

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

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

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

Iddifferenzja w.r.t. x

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