Issolvi 6x^3/12x^3-24x^2

$$\frac { 6 x ^ { 3 } } { 12 x ^ { 3 } - 24 x ^ { 2 } }$$

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Iffattura l-espressjonijiet li mhumiex diġà fatturati.

$$\frac{6x^{3}}{12\left(x-2\right)x^{2}}$$

Annulla 6x^{2} fin-numeratur u d-denominatur.

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

Espandi l-espressjoni.

$$\frac{x}{2x-4}$$

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

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.

$$\frac{\left(12x^{3}-24x^{2}\right)\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3})-6x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3}-24x^{2})}{\left(12x^{3}-24x^{2}\right)^{2}}$$

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}.

$$\frac{\left(12x^{3}-24x^{2}\right)\times 3\times 6x^{3-1}-6x^{3}\left(3\times 12x^{3-1}+2\left(-24\right)x^{2-1}\right)}{\left(12x^{3}-24x^{2}\right)^{2}}$$

Issimplifika.

$$\frac{\left(12x^{3}-24x^{2}\right)\times 18x^{2}-6x^{3}\left(36x^{2}-48x^{1}\right)}{\left(12x^{3}-24x^{2}\right)^{2}}$$

Immultiplika 12x^{3}-24x^{2} b'18x^{2}.

$$\frac{12x^{3}\times 18x^{2}-24x^{2}\times 18x^{2}-6x^{3}\left(36x^{2}-48x^{1}\right)}{\left(12x^{3}-24x^{2}\right)^{2}}$$

Immultiplika 6x^{3} b'36x^{2}-48x^{1}.

$$\frac{12x^{3}\times 18x^{2}-24x^{2}\times 18x^{2}-\left(6x^{3}\times 36x^{2}+6x^{3}\left(-48\right)x^{1}\right)}{\left(12x^{3}-24x^{2}\right)^{2}}$$

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

$$\frac{12\times 18x^{3+2}-24\times 18x^{2+2}-\left(6\times 36x^{3+2}+6\left(-48\right)x^{3+1}\right)}{\left(12x^{3}-24x^{2}\right)^{2}}$$

Issimplifika.

$$\frac{216x^{5}-432x^{4}-\left(216x^{5}-288x^{4}\right)}{\left(12x^{3}-24x^{2}\right)^{2}}$$

Ikkombina termini simili.

$$\frac{-144x^{4}}{\left(12x^{3}-24x^{2}\right)^{2}}$$