Issolvi a/(x+2)*x/(2x-1)

$$\frac { a } { ( x + 2 ) } \times \frac { x } { ( 2 x - 1 ) }$$

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Immultiplika \frac{a}{x+2} b'\frac{x}{2x-1} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' x+2 b'kull terminu ta' 2x-1.

$$\frac{ax}{2x^{2}-x+4x-2}$$

Ikkombina -x u 4x biex tikseb 3x.

$$\frac{ax}{2x^{2}+3x-2}$$

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Immultiplika \frac{a}{x+2} b'\frac{x}{2x-1} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' x+2 b'kull terminu ta' 2x-1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{ax}{2x^{2}-x+4x-2})$$

Ikkombina -x u 4x biex tikseb 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{ax}{2x^{2}+3x-2})$$

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.

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

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}.

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

Issimplifika.

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

Immultiplika 2x^{2}+3x^{1}-2 b'ax^{0}.

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

Immultiplika ax^{1} b'4x^{1}+3x^{0}.

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

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

$$\frac{2ax^{2}+3ax^{1}-2ax^{0}-\left(a\times 4x^{1+1}+a\times 3x^{1}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

Issimplifika.

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

Ikkombina termini simili.

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

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{\left(-2a\right)x^{2}+\left(-2a\right)x^{0}}{\left(2x^{2}+3x-2\right)^{2}}$$

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

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

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

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