Issolvi 3/2x*(x^2/6x+10)

$$\frac{ 3 }{ 2x } \times ( \frac{ { x }^{ 2 } }{ 6x+10 } )$$

Evalwa

$$\frac{3x}{4\left(3x+5\right)}$$

Passi Qosra tas-Soluzzjonijiet

Immultiplika \frac{3}{2x} b'\frac{x^{2}}{6x+10} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{3x^{2}}{2x\left(6x+10\right)}$$

Annulla x fin-numeratur u d-denominatur.

$$\frac{3x}{2\left(6x+10\right)}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'6x+10.

$$\frac{3x}{12x+20}$$

Iddifferenzja w.r.t. x

$$\frac{15}{4\left(3x+5\right)^{2}}$$

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Immultiplika \frac{3}{2x} b'\frac{x^{2}}{6x+10} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{2}}{2x\left(6x+10\right)})$$

Annulla x fin-numeratur u d-denominatur.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x}{2\left(6x+10\right)})$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'6x+10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x}{12x+20})$$

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.

$$\frac{\left(12x^{1}+20\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1})-3x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(12x^{1}+20)}{\left(12x^{1}+20\right)^{2}}$$

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}.

$$\frac{\left(12x^{1}+20\right)\times 3x^{1-1}-3x^{1}\times 12x^{1-1}}{\left(12x^{1}+20\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{\left(12x^{1}+20\right)\times 3x^{0}-3x^{1}\times 12x^{0}}{\left(12x^{1}+20\right)^{2}}$$

Espandi bl-użu ta' propjetà distributtiva.

$$\frac{12x^{1}\times 3x^{0}+20\times 3x^{0}-3x^{1}\times 12x^{0}}{\left(12x^{1}+20\right)^{2}}$$

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

$$\frac{12\times 3x^{1}+20\times 3x^{0}-3\times 12x^{1}}{\left(12x^{1}+20\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{36x^{1}+60x^{0}-36x^{1}}{\left(12x^{1}+20\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(36-36\right)x^{1}+60x^{0}}{\left(12x^{1}+20\right)^{2}}$$

Naqqas 36 minn 36.

$$\frac{60x^{0}}{\left(12x^{1}+20\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{60x^{0}}{\left(12x+20\right)^{2}}$$

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

$$\frac{60\times 1}{\left(12x+20\right)^{2}}$$

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

$$\frac{60}{\left(12x+20\right)^{2}}$$