Issolvi 1/y{frac{1/2x}}*1/2x/frac{1{y}}

$$\frac{ 1 }{ \frac{ y }{ \frac{ 1 }{ 2x } } } \times \frac{ \frac{ 1 }{ 2x } }{ \frac{ 1 }{ y } }$$

Evalwa

$$\frac{1}{4x^{2}}$$

Passi tas-Soluzzjonijiet

Iddividi 1 b'\frac{y}{\frac{1}{2x}} billi timmultiplika 1 bir-reċiproku ta' \frac{y}{\frac{1}{2x}}.

$$\frac{\frac{1}{2x}}{y}\times \frac{\frac{1}{2x}}{\frac{1}{y}}$$

Esprimi \frac{\frac{1}{2x}}{y} bħala frazzjoni waħda.

$$\frac{1}{2xy}\times \frac{\frac{1}{2x}}{\frac{1}{y}}$$

Iddividi \frac{1}{2x} b'\frac{1}{y} billi timmultiplika \frac{1}{2x} bir-reċiproku ta' \frac{1}{y}.

$$\frac{1}{2xy}\times \frac{y}{2x}$$

Immultiplika \frac{1}{2xy} b'\frac{y}{2x} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{y}{2xy\times 2x}$$

Annulla y fin-numeratur u d-denominatur.

$$\frac{1}{2\times 2xx}$$

Immultiplika x u x biex tikseb x^{2}.

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

Immultiplika 2 u 2 biex tikseb 4.

$$\frac{1}{4x^{2}}$$

Iddifferenzja w.r.t. x

$$-\frac{1}{2x^{3}}$$

Passi għall-Użu tar-Regola tal-Katina

Iddividi 1 b'\frac{y}{\frac{1}{2x}} billi timmultiplika 1 bir-reċiproku ta' \frac{y}{\frac{1}{2x}}.

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

Esprimi \frac{\frac{1}{2x}}{y} bħala frazzjoni waħda.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2xy}\times \frac{\frac{1}{2x}}{\frac{1}{y}})$$

Iddividi \frac{1}{2x} b'\frac{1}{y} billi timmultiplika \frac{1}{2x} bir-reċiproku ta' \frac{1}{y}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2xy}\times \frac{y}{2x})$$

Immultiplika \frac{1}{2xy} b'\frac{y}{2x} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y}{2xy\times 2x})$$

Annulla y fin-numeratur u d-denominatur.

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

Immultiplika x u x biex tikseb x^{2}.

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

Immultiplika 2 u 2 biex tikseb 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4x^{2}})$$

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).

$$-\left(4x^{2}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2})$$

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}.

$$-\left(4x^{2}\right)^{-2}\times 2\times 4x^{2-1}$$

Issimplifika.

$$-8x^{1}\times \left(4x^{2}\right)^{-2}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$-8x\times \left(4x^{2}\right)^{-2}$$