Issolvi 1/x-1/x+1=

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

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' x u x+1 huwa x\left(x+1\right). Immultiplika \frac{1}{x} b'\frac{x+1}{x+1}. Immultiplika \frac{1}{x+1} b'\frac{x}{x}.

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

Billi \frac{x+1}{x\left(x+1\right)} u \frac{x}{x\left(x+1\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Ikkombina termini simili f'x+1-x.

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

Espandi x\left(x+1\right).

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

Iddifferenzja w.r.t. x

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

Passi għall-Użu tar-Regola tal-Katina

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' x u x+1 huwa x\left(x+1\right). Immultiplika \frac{1}{x} b'\frac{x+1}{x+1}. Immultiplika \frac{1}{x+1} b'\frac{x}{x}.

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

Billi \frac{x+1}{x\left(x+1\right)} u \frac{x}{x\left(x+1\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Ikkombina termini simili f'x+1-x.

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

Uża l-propjetà distributtiva biex timmultiplika x b'x+1.

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

Jekk F hija l-kompożizzjoni ta' żewġ funzjonijiet differenzjabbli f\left(u\right) u u=g\left(x\right), jiġifieri, jekk F\left(x\right)=f\left(g\left(x\right)\right), mela d-derivattiv ta' F huwa d-derivattiv ta' f fir-rigward ta' u immultiplikat bid-derivattiv ta' g fir-rigward ta' x, jiġifieri, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

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}.

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

Issimplifika.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

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

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