Issolvi 2x+3+2/x+1

$$2 x + 3 + \frac { 2 } { x + 1 }$$

Evalwa

$$\frac{2x^{2}+5x+5}{x+1}$$

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 2x+3 b'\frac{x+1}{x+1}.

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

Billi \frac{\left(2x+3\right)\left(x+1\right)}{x+1} u \frac{2}{x+1} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi \left(2x+3\right)\left(x+1\right)+2.

$$\frac{2x^{2}+2x+3x+3+2}{x+1}$$

Ikkombina termini simili f'2x^{2}+2x+3x+3+2.

$$\frac{2x^{2}+5x+5}{x+1}$$

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 2x+3 b'\frac{x+1}{x+1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(2x+3\right)\left(x+1\right)}{x+1}+\frac{2}{x+1})$$

Billi \frac{\left(2x+3\right)\left(x+1\right)}{x+1} u \frac{2}{x+1} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(2x+3\right)\left(x+1\right)+2}{x+1})$$

Agħmel il-multiplikazzjonijiet fi \left(2x+3\right)\left(x+1\right)+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}+2x+3x+3+2}{x+1})$$

Ikkombina termini simili f'2x^{2}+2x+3x+3+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}+5x+5}{x+1})$$

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.

$$\frac{\left(x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+5x^{1}+5)-\left(2x^{2}+5x^{1}+5\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+1)}{\left(x^{1}+1\right)^{2}}$$

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}.

$$\frac{\left(x^{1}+1\right)\left(2\times 2x^{2-1}+5x^{1-1}\right)-\left(2x^{2}+5x^{1}+5\right)x^{1-1}}{\left(x^{1}+1\right)^{2}}$$

Issimplifika.

$$\frac{\left(x^{1}+1\right)\left(4x^{1}+5x^{0}\right)-\left(2x^{2}+5x^{1}+5\right)x^{0}}{\left(x^{1}+1\right)^{2}}$$

Immultiplika x^{1}+1 b'4x^{1}+5x^{0}.

$$\frac{x^{1}\times 4x^{1}+x^{1}\times 5x^{0}+4x^{1}+5x^{0}-\left(2x^{2}+5x^{1}+5\right)x^{0}}{\left(x^{1}+1\right)^{2}}$$

Immultiplika 2x^{2}+5x^{1}+5 b'x^{0}.

$$\frac{x^{1}\times 4x^{1}+x^{1}\times 5x^{0}+4x^{1}+5x^{0}-\left(2x^{2}x^{0}+5x^{1}x^{0}+5x^{0}\right)}{\left(x^{1}+1\right)^{2}}$$

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

$$\frac{4x^{1+1}+5x^{1}+4x^{1}+5x^{0}-\left(2x^{2}+5x^{1}+5x^{0}\right)}{\left(x^{1}+1\right)^{2}}$$

Issimplifika.

$$\frac{4x^{2}+5x^{1}+4x^{1}+5x^{0}-\left(2x^{2}+5x^{1}+5x^{0}\right)}{\left(x^{1}+1\right)^{2}}$$

Ikkombina termini simili.

$$\frac{2x^{2}+4x^{1}}{\left(x^{1}+1\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{2x^{2}+4x}{\left(x+1\right)^{2}}$$