Issolvi (3g^2/5-7g^1/6)-(g^2/5-3g^1/6)

$$( 3 g ^ { 2 / 5 } - 7 g ^ { 1 / 6 } ) - ( g ^ { 2 / 5 } - 3 g ^ { 1 / 6 } )$$

Evalwa

$$2g^{\frac{2}{5}}-4\sqrt[6]{g}$$

Passi tas-Soluzzjonijiet

Biex issib l-oppost ta' g^{\frac{2}{5}}-3g^{\frac{1}{6}}, sib l-oppost ta' kull terminu.

$$3g^{\frac{2}{5}}-7g^{\frac{1}{6}}-g^{\frac{2}{5}}+3g^{\frac{1}{6}}$$

Ikkombina 3g^{\frac{2}{5}} u -g^{\frac{2}{5}} biex tikseb 2g^{\frac{2}{5}}.

$$2g^{\frac{2}{5}}-7g^{\frac{1}{6}}+3g^{\frac{1}{6}}$$

Ikkombina -7g^{\frac{1}{6}} u 3g^{\frac{1}{6}} biex tikseb -4g^{\frac{1}{6}}.

$$2g^{\frac{2}{5}}-4g^{\frac{1}{6}}$$

Iddifferenzja w.r.t. g

$$\frac{4}{5g^{\frac{3}{5}}}-\frac{2}{3g^{\frac{5}{6}}}$$

Passi għall-Użu ta' Regola Derivattiva għal Somma

Biex issib l-oppost ta' g^{\frac{2}{5}}-3g^{\frac{1}{6}}, sib l-oppost ta' kull terminu.

$$\frac{\mathrm{d}}{\mathrm{d}g}(3g^{\frac{2}{5}}-7g^{\frac{1}{6}}-g^{\frac{2}{5}}+3g^{\frac{1}{6}})$$

Ikkombina 3g^{\frac{2}{5}} u -g^{\frac{2}{5}} biex tikseb 2g^{\frac{2}{5}}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(2g^{\frac{2}{5}}-7g^{\frac{1}{6}}+3g^{\frac{1}{6}})$$

Ikkombina -7g^{\frac{1}{6}} u 3g^{\frac{1}{6}} biex tikseb -4g^{\frac{1}{6}}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(2g^{\frac{2}{5}}-4g^{\frac{1}{6}})$$

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}.

$$\frac{2}{5}\times 2g^{\frac{2}{5}-1}+\frac{1}{6}\left(-4\right)g^{\frac{1}{6}-1}$$

Immultiplika \frac{2}{5} b'2.

$$\frac{4}{5}g^{\frac{2}{5}-1}+\frac{1}{6}\left(-4\right)g^{\frac{1}{6}-1}$$

Naqqas 1 minn \frac{2}{5}.

$$\frac{4}{5}g^{-\frac{3}{5}}+\frac{1}{6}\left(-4\right)g^{\frac{1}{6}-1}$$

Immultiplika \frac{1}{6} b'-4.

$$\frac{4}{5}g^{-\frac{3}{5}}-\frac{2}{3}g^{\frac{1}{6}-1}$$

Naqqas 1 minn \frac{1}{6}.

$$\frac{4}{5}g^{-\frac{3}{5}}-\frac{2}{3}g^{-\frac{5}{6}}$$