Issolvi x^199/x^200+100

$$\frac { x ^ { 199 } } { x ^ { 200 } + 100 }$$

Iddifferenzja w.r.t. x

$$\frac{x^{198}\left(19900-x^{200}\right)}{\left(x^{200}+100\right)^{2}}$$

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.

$$\frac{\left(x^{200}+100\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{199})-x^{199}\frac{\mathrm{d}}{\mathrm{d}x}(x^{200}+100)}{\left(x^{200}+100\right)^{2}}$$

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}.

$$\frac{\left(x^{200}+100\right)\times 199x^{199-1}-x^{199}\times 200x^{200-1}}{\left(x^{200}+100\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{\left(x^{200}+100\right)\times 199x^{198}-x^{199}\times 200x^{199}}{\left(x^{200}+100\right)^{2}}$$

Espandi bl-użu ta' propjetà distributtiva.

$$\frac{x^{200}\times 199x^{198}+100\times 199x^{198}-x^{199}\times 200x^{199}}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{199x^{200+198}+100\times 199x^{198}-200x^{199+199}}{\left(x^{200}+100\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{199x^{398}+19900x^{198}-200x^{398}}{\left(x^{200}+100\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(199-200\right)x^{398}+19900x^{198}}{\left(x^{200}+100\right)^{2}}$$

Naqqas 200 minn 199.

$$\frac{-x^{398}+19900x^{198}}{\left(x^{200}+100\right)^{2}}$$

Iffattura 'l barra x^{198}.

$$\frac{x^{198}\left(-x^{200}+19900x^{0}\right)}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{x^{198}\left(-x^{200}+19900\times 1\right)}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{x^{198}\left(-x^{200}+19900\right)}{\left(x^{200}+100\right)^{2}}$$

Evalwa

$$\frac{x^{199}}{x^{200}+100}$$