Issolvi f(x)=1/x+1+1

$$f ( x ) = \frac { 1 } { x + 1 } + 1$$

Evalwa

$$\frac{x+2}{x+1}$$

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 1 b'\frac{x+1}{x+1}.

$$\frac{1}{x+1}+\frac{x+1}{x+1}$$

Billi \frac{1}{x+1} u \frac{x+1}{x+1} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{1+x+1}{x+1}$$

Ikkombina termini simili f'1+x+1.

$$\frac{2+x}{x+1}$$

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 1 b'\frac{x+1}{x+1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x+1}+\frac{x+1}{x+1})$$

Billi \frac{1}{x+1} u \frac{x+1}{x+1} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1+x+1}{x+1})$$

Ikkombina termini simili f'1+x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2+x}{x+1})$$

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.

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

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}.

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

Agħmel l-aritmetika.

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

Espandi bl-użu ta' propjetà distributtiva.

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

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

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

Neħħi l-parenteżi mhux meħtieġa.

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

Ikkombina termini simili.

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

Naqqas 1 minn 1 u 2 minn 1.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

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

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