Issolvi y-2/x-3/x^2

$$y - \frac { 2 } { x } - \frac { 3 } { x ^ { 2 } }$$

Iddifferenzja w.r.t. x

$$\frac{2\left(x+3\right)}{x^{3}}$$

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{yx}{x}-\frac{2}{x}-\frac{3}{x^{2}})$$

Billi \frac{yx}{x} u \frac{2}{x} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{yx-2}{x}-\frac{3}{x^{2}})$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' x u x^{2} huwa x^{2}. Immultiplika \frac{yx-2}{x} b'\frac{x}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(yx-2\right)x}{x^{2}}-\frac{3}{x^{2}})$$

Billi \frac{\left(yx-2\right)x}{x^{2}} u \frac{3}{x^{2}} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(yx-2\right)x-3}{x^{2}})$$

Agħmel il-multiplikazzjonijiet fi \left(yx-2\right)x-3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{yx^{2}-2x-3}{x^{2}})$$

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.

$$\frac{x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(yx^{2}-2x^{1}-3)-\left(yx^{2}-2x^{1}-3\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2})}{\left(x^{2}\right)^{2}}$$

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}.

$$\frac{x^{2}\left(2yx^{2-1}-2x^{1-1}\right)-\left(yx^{2}-2x^{1}-3\right)\times 2x^{2-1}}{\left(x^{2}\right)^{2}}$$

Issimplifika.

$$\frac{x^{2}\left(2yx^{1}-2x^{0}\right)-\left(yx^{2}-2x^{1}-3\right)\times 2x^{1}}{\left(x^{2}\right)^{2}}$$

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

$$\frac{x^{2}\times 2yx^{1}+x^{2}\left(-2\right)x^{0}-\left(yx^{2}-2x^{1}-3\right)\times 2x^{1}}{\left(x^{2}\right)^{2}}$$

Immultiplika yx^{2}-2x^{1}-3 b'2x^{1}.

$$\frac{x^{2}\times 2yx^{1}+x^{2}\left(-2\right)x^{0}-\left(yx^{2}\times 2x^{1}-2x^{1}\times 2x^{1}-3\times 2x^{1}\right)}{\left(x^{2}\right)^{2}}$$

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

$$\frac{2yx^{2+1}-2x^{2}-\left(y\times 2x^{2+1}-2\times 2x^{1+1}-3\times 2x^{1}\right)}{\left(x^{2}\right)^{2}}$$

Issimplifika.

$$\frac{2yx^{3}-2x^{2}-\left(2yx^{3}-4x^{2}-6x^{1}\right)}{\left(x^{2}\right)^{2}}$$

Ikkombina termini simili.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

Evalwa

$$y-\frac{2}{x}-\frac{3}{x^{2}}$$