Issolvi 6x^2y/2x-6div30xy/5x-10

$$\frac { 6 x ^ { 2 } y } { 2 x - 6 } \div \frac { 30 x y } { 5 x - 10 }$$

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Iddividi \frac{6x^{2}y}{2x-6} b'\frac{30xy}{5x-10} billi timmultiplika \frac{6x^{2}y}{2x-6} bir-reċiproku ta' \frac{30xy}{5x-10}.

$$\frac{6x^{2}y\left(5x-10\right)}{\left(2x-6\right)\times 30xy}$$

Annulla 6xy fin-numeratur u d-denominatur.

$$\frac{x\left(5x-10\right)}{5\left(2x-6\right)}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati.

$$\frac{5x\left(x-2\right)}{2\times 5\left(x-3\right)}$$

Annulla 5 fin-numeratur u d-denominatur.

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

Espandi l-espressjoni.

$$\frac{x^{2}-2x}{2x-6}$$

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Iddividi \frac{6x^{2}y}{2x-6} b'\frac{30xy}{5x-10} billi timmultiplika \frac{6x^{2}y}{2x-6} bir-reċiproku ta' \frac{30xy}{5x-10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x^{2}y\left(5x-10\right)}{\left(2x-6\right)\times 30xy})$$

Annulla 6xy fin-numeratur u d-denominatur.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(5x-10\right)}{5\left(2x-6\right)})$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x\left(5x-10\right)}{5\left(2x-6\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x\left(x-2\right)}{2\times 5\left(x-3\right)})$$

Annulla 5 fin-numeratur u d-denominatur.

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}-2x}{2x-6})$$

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.

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

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}.

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

Issimplifika.

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

Immultiplika 2x^{1}-6 b'2x^{1}-2x^{0}.

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

Immultiplika x^{2}-2x^{1} b'2x^{0}.

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

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

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

Issimplifika.

$$\frac{4x^{2}-4x^{1}-12x^{1}+12x^{0}-\left(2x^{2}-4x^{1}\right)}{\left(2x^{1}-6\right)^{2}}$$

Ikkombina termini simili.

$$\frac{2x^{2}-12x^{1}+12x^{0}}{\left(2x^{1}-6\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{2x^{2}-12x+12x^{0}}{\left(2x-6\right)^{2}}$$

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

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

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

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