Issolvi 3x+2+1/3x+2

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

Evalwa

$$\frac{9x^{2}+12x+5}{3x+2}$$

Passi Qosra tas-Soluzzjonijiet

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

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

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

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

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

$$\frac{9x^{2}+6x+6x+4+1}{3x+2}$$

Ikkombina termini simili f'9x^{2}+6x+6x+4+1.

$$\frac{9x^{2}+12x+5}{3x+2}$$

Iddifferenzja w.r.t. x

$$\frac{9\left(x+1\right)\left(3x+1\right)}{\left(3x+2\right)^{2}}$$

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9x^{2}+6x+6x+4+1}{3x+2})$$

Ikkombina termini simili f'9x^{2}+6x+6x+4+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9x^{2}+12x+5}{3x+2})$$

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.

$$\frac{\left(3x^{1}+2\right)\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2}+12x^{1}+5)-\left(9x^{2}+12x^{1}+5\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1}+2)}{\left(3x^{1}+2\right)^{2}}$$

Id-derivattiv ta' polynomial huwa s-somma tad-derivattivi tat-termini tiegħu. Id-derivattiv ta' kwalunkwe terminu kostanti huwa 0. Id-derivattiv ta' ax^{n} huwa nax^{n-1}.

$$\frac{\left(3x^{1}+2\right)\left(2\times 9x^{2-1}+12x^{1-1}\right)-\left(9x^{2}+12x^{1}+5\right)\times 3x^{1-1}}{\left(3x^{1}+2\right)^{2}}$$

Issimplifika.

$$\frac{\left(3x^{1}+2\right)\left(18x^{1}+12x^{0}\right)-\left(9x^{2}+12x^{1}+5\right)\times 3x^{0}}{\left(3x^{1}+2\right)^{2}}$$

Immultiplika 3x^{1}+2 b'18x^{1}+12x^{0}.

$$\frac{3x^{1}\times 18x^{1}+3x^{1}\times 12x^{0}+2\times 18x^{1}+2\times 12x^{0}-\left(9x^{2}+12x^{1}+5\right)\times 3x^{0}}{\left(3x^{1}+2\right)^{2}}$$

Immultiplika 9x^{2}+12x^{1}+5 b'3x^{0}.

$$\frac{3x^{1}\times 18x^{1}+3x^{1}\times 12x^{0}+2\times 18x^{1}+2\times 12x^{0}-\left(9x^{2}\times 3x^{0}+12x^{1}\times 3x^{0}+5\times 3x^{0}\right)}{\left(3x^{1}+2\right)^{2}}$$

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

$$\frac{3\times 18x^{1+1}+3\times 12x^{1}+2\times 18x^{1}+2\times 12x^{0}-\left(9\times 3x^{2}+12\times 3x^{1}+5\times 3x^{0}\right)}{\left(3x^{1}+2\right)^{2}}$$

Issimplifika.

$$\frac{54x^{2}+36x^{1}+36x^{1}+24x^{0}-\left(27x^{2}+36x^{1}+15x^{0}\right)}{\left(3x^{1}+2\right)^{2}}$$

Ikkombina termini simili.

$$\frac{27x^{2}+36x^{1}+9x^{0}}{\left(3x^{1}+2\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{27x^{2}+36x+9x^{0}}{\left(3x+2\right)^{2}}$$

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

$$\frac{27x^{2}+36x+9\times 1}{\left(3x+2\right)^{2}}$$

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

$$\frac{27x^{2}+36x+9}{\left(3x+2\right)^{2}}$$