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

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

Arvuta

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

Lahenduse etapid

Avaldise "g^{\frac{2}{5}}-3g^{\frac{1}{6}}" vastandi leidmiseks tuleb leida iga liikme vastand.

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

Kombineerige 3g^{\frac{2}{5}} ja -g^{\frac{2}{5}}, et leida 2g^{\frac{2}{5}}.

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

Kombineerige -7g^{\frac{1}{6}} ja 3g^{\frac{1}{6}}, et leida -4g^{\frac{1}{6}}.

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

Diferentseeri g-i järgi

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

Juhised summa tuletisereegli kasutamisel

Avaldise "g^{\frac{2}{5}}-3g^{\frac{1}{6}}" vastandi leidmiseks tuleb leida iga liikme vastand.

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

Kombineerige 3g^{\frac{2}{5}} ja -g^{\frac{2}{5}}, et leida 2g^{\frac{2}{5}}.

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

Kombineerige -7g^{\frac{1}{6}} ja 3g^{\frac{1}{6}}, et leida -4g^{\frac{1}{6}}.

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

Polünoomi tuletis on polünoomi liikmete tuletiste summa. Mis tahes vabaliikme tuletis on 0. ax^{n} tuletis on nax^{n-1}.

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

Korrutage omavahel \frac{2}{5} ja 2.

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

Lahutage 1 väärtusest \frac{2}{5}.

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

Korrutage omavahel \frac{1}{6} ja -4.

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

Lahutage 1 väärtusest \frac{1}{6}.

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