Issolvi x+2/x+1

$$x + \frac { 2 } { x + 1 }$$

Evalwa

$$\frac{x^{2}+x+2}{x+1}$$

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika x b'\frac{x+1}{x+1}.

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

Billi \frac{x\left(x+1\right)}{x+1} u \frac{2}{x+1} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi x\left(x+1\right)+2.

$$\frac{x^{2}+x+2}{x+1}$$

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika x b'\frac{x+1}{x+1}.

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

Billi \frac{x\left(x+1\right)}{x+1} u \frac{2}{x+1} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi x\left(x+1\right)+2.

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

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.

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

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}.

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

Issimplifika.

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

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

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

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

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

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

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

Issimplifika.

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

Ikkombina termini simili.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

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

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