Issolvi x/x+5/frac{x{x+5}+5}

$$\frac { \frac { x } { x + 5 } } { \frac { x } { x + 5 } + 5 }$$

Evalwa

$$\frac{x}{6x+25}$$

Passi Qosra tas-Soluzzjonijiet

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

$$\frac{\frac{x}{x+5}}{\frac{x}{x+5}+\frac{5\left(x+5\right)}{x+5}}$$

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

$$\frac{\frac{x}{x+5}}{\frac{x+5\left(x+5\right)}{x+5}}$$

Agħmel il-multiplikazzjonijiet fi x+5\left(x+5\right).

$$\frac{\frac{x}{x+5}}{\frac{x+5x+25}{x+5}}$$

Ikkombina termini simili f'x+5x+25.

$$\frac{\frac{x}{x+5}}{\frac{6x+25}{x+5}}$$

Iddividi \frac{x}{x+5} b'\frac{6x+25}{x+5} billi timmultiplika \frac{x}{x+5} bir-reċiproku ta' \frac{6x+25}{x+5}.

$$\frac{x\left(x+5\right)}{\left(x+5\right)\left(6x+25\right)}$$

Annulla x+5 fin-numeratur u d-denominatur.

$$\frac{x}{6x+25}$$

Iddifferenzja w.r.t. x

$$\frac{25}{\left(6x+25\right)^{2}}$$

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{x+5}{x+5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{x+5}}{\frac{x}{x+5}+\frac{5\left(x+5\right)}{x+5}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{x+5}}{\frac{x+5\left(x+5\right)}{x+5}})$$

Agħmel il-multiplikazzjonijiet fi x+5\left(x+5\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{x+5}}{\frac{x+5x+25}{x+5}})$$

Ikkombina termini simili f'x+5x+25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{x+5}}{\frac{6x+25}{x+5}})$$

Iddividi \frac{x}{x+5} b'\frac{6x+25}{x+5} billi timmultiplika \frac{x}{x+5} bir-reċiproku ta' \frac{6x+25}{x+5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+5\right)}{\left(x+5\right)\left(6x+25\right)})$$

Annulla x+5 fin-numeratur u d-denominatur.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{6x+25})$$

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.

$$\frac{\left(6x^{1}+25\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(6x^{1}+25)}{\left(6x^{1}+25\right)^{2}}$$

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}.

$$\frac{\left(6x^{1}+25\right)x^{1-1}-x^{1}\times 6x^{1-1}}{\left(6x^{1}+25\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{\left(6x^{1}+25\right)x^{0}-x^{1}\times 6x^{0}}{\left(6x^{1}+25\right)^{2}}$$

Espandi bl-użu ta' propjetà distributtiva.

$$\frac{6x^{1}x^{0}+25x^{0}-x^{1}\times 6x^{0}}{\left(6x^{1}+25\right)^{2}}$$

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

$$\frac{6x^{1}+25x^{0}-6x^{1}}{\left(6x^{1}+25\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(6-6\right)x^{1}+25x^{0}}{\left(6x^{1}+25\right)^{2}}$$

Naqqas 6 minn 6.

$$\frac{25x^{0}}{\left(6x^{1}+25\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{25x^{0}}{\left(6x+25\right)^{2}}$$

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

$$\frac{25\times 1}{\left(6x+25\right)^{2}}$$

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

$$\frac{25}{\left(6x+25\right)^{2}}$$