Issolvi 2x^2/1-6x

$$\frac{ 2 { x }^{ 2 } }{ 1-6x }$$

Iddifferenzja w.r.t. x

$$-\frac{4x\left(3x-1\right)}{\left(6x-1\right)^{2}}$$

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.

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

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}.

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

Agħmel l-aritmetika.

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

Espandi bl-użu ta' propjetà distributtiva.

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

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

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

Agħmel l-aritmetika.

$$\frac{-24x^{2}+4x^{1}-\left(-12x^{2}\right)}{\left(-6x^{1}+1\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(-24-\left(-12\right)\right)x^{2}+4x^{1}}{\left(-6x^{1}+1\right)^{2}}$$

Naqqas -12 minn -24.

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

Iffattura 'l barra 4x.

$$\frac{4x\left(-3x^{1}+x^{0}\right)}{\left(-6x^{1}+1\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{4x\left(-3x+x^{0}\right)}{\left(-6x+1\right)^{2}}$$

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

$$\frac{4x\left(-3x+1\right)}{\left(-6x+1\right)^{2}}$$

Evalwa

$$\frac{2x^{2}}{1-6x}$$