Issolvi 2/(frac{2{x+3})+3}

$$\frac { 2 } { ( \frac { 2 } { x + 3 } ) + 3 }$$

Evalwa

$$\frac{2\left(x+3\right)}{3x+11}$$

Passi Qosra tas-Soluzzjonijiet

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

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

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

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

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

$$\frac{2}{\frac{2+3x+9}{x+3}}$$

Ikkombina termini simili f'2+3x+9.

$$\frac{2}{\frac{11+3x}{x+3}}$$

Iddividi 2 b'\frac{11+3x}{x+3} billi timmultiplika 2 bir-reċiproku ta' \frac{11+3x}{x+3}.

$$\frac{2\left(x+3\right)}{11+3x}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'x+3.

$$\frac{2x+6}{11+3x}$$

Iddifferenzja w.r.t. x

$$\frac{4}{\left(3x+11\right)^{2}}$$

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

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

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

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

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

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

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

Ikkombina termini simili f'2+3x+9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{\frac{11+3x}{x+3}})$$

Iddividi 2 b'\frac{11+3x}{x+3} billi timmultiplika 2 bir-reċiproku ta' \frac{11+3x}{x+3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x+3\right)}{11+3x})$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'x+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+6}{11+3x})$$

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.

$$\frac{\left(3x^{1}+11\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+6)-\left(2x^{1}+6\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1}+11)}{\left(3x^{1}+11\right)^{2}}$$

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}.

$$\frac{\left(3x^{1}+11\right)\times 2x^{1-1}-\left(2x^{1}+6\right)\times 3x^{1-1}}{\left(3x^{1}+11\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{\left(3x^{1}+11\right)\times 2x^{0}-\left(2x^{1}+6\right)\times 3x^{0}}{\left(3x^{1}+11\right)^{2}}$$

Espandi bl-użu ta' propjetà distributtiva.

$$\frac{3x^{1}\times 2x^{0}+11\times 2x^{0}-\left(2x^{1}\times 3x^{0}+6\times 3x^{0}\right)}{\left(3x^{1}+11\right)^{2}}$$

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

$$\frac{3\times 2x^{1}+11\times 2x^{0}-\left(2\times 3x^{1}+6\times 3x^{0}\right)}{\left(3x^{1}+11\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{6x^{1}+22x^{0}-\left(6x^{1}+18x^{0}\right)}{\left(3x^{1}+11\right)^{2}}$$

Neħħi l-parenteżi mhux meħtieġa.

$$\frac{6x^{1}+22x^{0}-6x^{1}-18x^{0}}{\left(3x^{1}+11\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(6-6\right)x^{1}+\left(22-18\right)x^{0}}{\left(3x^{1}+11\right)^{2}}$$

Naqqas 6 minn 6 u 18 minn 22.

$$\frac{4x^{0}}{\left(3x^{1}+11\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{4x^{0}}{\left(3x+11\right)^{2}}$$

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

$$\frac{4\times 1}{\left(3x+11\right)^{2}}$$

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

$$\frac{4}{\left(3x+11\right)^{2}}$$