Issolvi 2r/r+10+5

$$\frac { 2 r } { r + 10 } + 5$$

Evalwa

$$\frac{7r+50}{r+10}$$

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 5 b'\frac{r+10}{r+10}.

$$\frac{2r}{r+10}+\frac{5\left(r+10\right)}{r+10}$$

Billi \frac{2r}{r+10} u \frac{5\left(r+10\right)}{r+10} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{2r+5\left(r+10\right)}{r+10}$$

Agħmel il-multiplikazzjonijiet fi 2r+5\left(r+10\right).

$$\frac{2r+5r+50}{r+10}$$

Ikkombina termini simili f'2r+5r+50.

$$\frac{7r+50}{r+10}$$

Iddifferenzja w.r.t. r

$$\frac{20}{\left(r+10\right)^{2}}$$

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 5 b'\frac{r+10}{r+10}.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r}{r+10}+\frac{5\left(r+10\right)}{r+10})$$

Billi \frac{2r}{r+10} u \frac{5\left(r+10\right)}{r+10} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r+5\left(r+10\right)}{r+10})$$

Agħmel il-multiplikazzjonijiet fi 2r+5\left(r+10\right).

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r+5r+50}{r+10})$$

Ikkombina termini simili f'2r+5r+50.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{7r+50}{r+10})$$

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.

$$\frac{\left(r^{1}+10\right)\frac{\mathrm{d}}{\mathrm{d}r}(7r^{1}+50)-\left(7r^{1}+50\right)\frac{\mathrm{d}}{\mathrm{d}r}(r^{1}+10)}{\left(r^{1}+10\right)^{2}}$$

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}.

$$\frac{\left(r^{1}+10\right)\times 7r^{1-1}-\left(7r^{1}+50\right)r^{1-1}}{\left(r^{1}+10\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{\left(r^{1}+10\right)\times 7r^{0}-\left(7r^{1}+50\right)r^{0}}{\left(r^{1}+10\right)^{2}}$$

Espandi bl-użu ta' propjetà distributtiva.

$$\frac{r^{1}\times 7r^{0}+10\times 7r^{0}-\left(7r^{1}r^{0}+50r^{0}\right)}{\left(r^{1}+10\right)^{2}}$$

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

$$\frac{7r^{1}+10\times 7r^{0}-\left(7r^{1}+50r^{0}\right)}{\left(r^{1}+10\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{7r^{1}+70r^{0}-\left(7r^{1}+50r^{0}\right)}{\left(r^{1}+10\right)^{2}}$$

Neħħi l-parenteżi mhux meħtieġa.

$$\frac{7r^{1}+70r^{0}-7r^{1}-50r^{0}}{\left(r^{1}+10\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(7-7\right)r^{1}+\left(70-50\right)r^{0}}{\left(r^{1}+10\right)^{2}}$$

Naqqas 7 minn 7 u 50 minn 70.

$$\frac{20r^{0}}{\left(r^{1}+10\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{20r^{0}}{\left(r+10\right)^{2}}$$

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

$$\frac{20\times 1}{\left(r+10\right)^{2}}$$

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

$$\frac{20}{\left(r+10\right)^{2}}$$