Issolvi 8y/12y-18y^2

$$\frac { 8 y } { 12 y - 18 y ^ { 2 } }$$

Evalwa

$$\frac{4}{3\left(2-3y\right)}$$

Passi Qosra tas-Soluzzjonijiet

Iffattura l-espressjonijiet li mhumiex diġà fatturati.

$$\frac{8y}{6y\left(-3y+2\right)}$$

Annulla 2y fin-numeratur u d-denominatur.

$$\frac{4}{3\left(-3y+2\right)}$$

Espandi l-espressjoni.

$$\frac{4}{-9y+6}$$

Iddifferenzja w.r.t. y

$$\frac{4}{\left(2-3y\right)^{2}}$$

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.

$$\frac{\left(12y^{1}-18y^{2}\right)\frac{\mathrm{d}}{\mathrm{d}y}(8y^{1})-8y^{1}\frac{\mathrm{d}}{\mathrm{d}y}(12y^{1}-18y^{2})}{\left(12y^{1}-18y^{2}\right)^{2}}$$

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}.

$$\frac{\left(12y^{1}-18y^{2}\right)\times 8y^{1-1}-8y^{1}\left(12y^{1-1}+2\left(-18\right)y^{2-1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

Issimplifika.

$$\frac{\left(12y^{1}-18y^{2}\right)\times 8y^{0}-8y^{1}\left(12y^{0}-36y^{1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

Immultiplika 12y^{1}-18y^{2} b'8y^{0}.

$$\frac{12y^{1}\times 8y^{0}-18y^{2}\times 8y^{0}-8y^{1}\left(12y^{0}-36y^{1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

Immultiplika 8y^{1} b'12y^{0}-36y^{1}.

$$\frac{12y^{1}\times 8y^{0}-18y^{2}\times 8y^{0}-\left(8y^{1}\times 12y^{0}+8y^{1}\left(-36\right)y^{1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

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

$$\frac{12\times 8y^{1}-18\times 8y^{2}-\left(8\times 12y^{1}+8\left(-36\right)y^{1+1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

Issimplifika.

$$\frac{96y^{1}-144y^{2}-\left(96y^{1}-288y^{2}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

Ikkombina termini simili.

$$\frac{144y^{2}}{\left(12y^{1}-18y^{2}\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{144y^{2}}{\left(12y-18y^{2}\right)^{2}}$$