Issolvi (x/x+1-x/x-1)1-x^2/2

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

Evalwa

$$x$$

Passi Qosra tas-Soluzzjonijiet

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

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

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

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

Agħmel il-multiplikazzjonijiet fi x\left(x-1\right)-x\left(x+1\right).

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

Ikkombina termini simili f'x^{2}-x-x^{2}-x.

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

Immultiplika \frac{-2x}{\left(x-1\right)\left(x+1\right)} b'\frac{1-x^{2}}{2} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Annulla 2 fin-numeratur u d-denominatur.

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

Iffattura l-espressjonijiet li mhumiex diġà fatturati.

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

Estratta l-sinjal negattiv fi -1-x.

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

Annulla \left(x-1\right)\left(x+1\right) fin-numeratur u d-denominatur.

$$-\left(-1\right)x$$

Espandi l-espressjoni.

$$x$$

Iddifferenzja w.r.t. x

$$1$$

Passi għall-Użu ta' Definizzjoni ta' Dervattiv

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

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

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

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

Agħmel il-multiplikazzjonijiet fi x\left(x-1\right)-x\left(x+1\right).

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

Ikkombina termini simili f'x^{2}-x-x^{2}-x.

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

Immultiplika \frac{-2x}{\left(x-1\right)\left(x+1\right)} b'\frac{1-x^{2}}{2} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Annulla 2 fin-numeratur u d-denominatur.

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

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{-x\left(-x^{2}+1\right)}{\left(x-1\right)\left(x+1\right)}.

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

Estratta l-sinjal negattiv fi -1-x.

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

Annulla \left(x-1\right)\left(x+1\right) fin-numeratur u d-denominatur.

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

Espandi l-espressjoni.

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

Id-derivattiv ta' ax^{n} huwa nax^{n-1}.

$$x^{1-1}$$

Naqqas 1 minn 1.

$$x^{0}$$

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

$$1$$