Issolvi d/dxx^2(2+x)/x^2-x

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

Evalwa

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x^{2}\left(2+x\right)}{x^{2}-x}.

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

Annulla x fin-numeratur u d-denominatur.

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

Uża l-propjetà distributtiva biex timmultiplika x b'x+2.

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

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.

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

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}.

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

Issimplifika.

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

Immultiplika x^{1}-1 b'2x^{1}+2x^{0}.

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

Immultiplika x^{2}+2x^{1} b'x^{0}.

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

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

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

Issimplifika.

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

Ikkombina termini simili.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

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

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

Iddifferenzja w.r.t. x

$$\frac{6}{\left(x-1\right)^{3}}$$