Issolvi 1/x^2-2x+5dx

$$\frac { 1 } { x ^ { 2 } - 2 x + 5 } d x$$

Evalwa

$$\frac{dx}{x^{2}-2x+5}$$

Passi tas-Soluzzjonijiet

Esprimi \frac{1}{x^{2}-2x+5}d bħala frazzjoni waħda.

$$\frac{d}{x^{2}-2x+5}x$$

Esprimi \frac{d}{x^{2}-2x+5}x bħala frazzjoni waħda.

$$\frac{dx}{x^{2}-2x+5}$$

Iddifferenzja w.r.t. x

$$\frac{d\left(5-x^{2}\right)}{\left(x^{2}-2x+5\right)^{2}}$$

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Esprimi \frac{1}{x^{2}-2x+5}d bħala frazzjoni waħda.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{d}{x^{2}-2x+5}x)$$

Esprimi \frac{d}{x^{2}-2x+5}x bħala frazzjoni waħda.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{dx}{x^{2}-2x+5})$$

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.

$$\frac{\left(x^{2}-2x^{1}+5\right)\frac{\mathrm{d}}{\mathrm{d}x}(dx^{1})-dx^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-2x^{1}+5)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-2x^{1}+5\right)dx^{1-1}-dx^{1}\left(2x^{2-1}-2x^{1-1}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Issimplifika.

$$\frac{\left(x^{2}-2x^{1}+5\right)dx^{0}-dx^{1}\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Immultiplika x^{2}-2x^{1}+5 b'dx^{0}.

$$\frac{x^{2}dx^{0}-2x^{1}dx^{0}+5dx^{0}-dx^{1}\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Immultiplika dx^{1} b'2x^{1}-2x^{0}.

$$\frac{x^{2}dx^{0}-2x^{1}dx^{0}+5dx^{0}-\left(dx^{1}\times 2x^{1}+dx^{1}\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

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

$$\frac{dx^{2}-2dx^{1}+5dx^{0}-\left(d\times 2x^{1+1}+d\left(-2\right)x^{1}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Issimplifika.

$$\frac{dx^{2}+\left(-2d\right)x^{1}+5dx^{0}-\left(2dx^{2}+\left(-2d\right)x^{1}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(-d\right)x^{2}+5dx^{0}}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{\left(-d\right)x^{2}+5dx^{0}}{\left(x^{2}-2x+5\right)^{2}}$$

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

$$\frac{\left(-d\right)x^{2}+5d\times 1}{\left(x^{2}-2x+5\right)^{2}}$$

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

$$\frac{\left(-d\right)x^{2}+5d}{\left(x^{2}-2x+5\right)^{2}}$$