derivative x(2x+7)^{1/3}

Lösung

ableitung von

x (2 x + 7)^{\frac{1}{3}}

\frac{8 x + 21}{3 ( 2 x + 7 ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (x (2 x + 7)^{\frac{1}{3}})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (2 x + 7)^{\frac{1}{3}}

= \frac{d x}{d x} (2 x + 7)^{\frac{1}{3}} + \frac{d}{d x} ((2 x + 7)^{\frac{1}{3}}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((2 x + 7)^{\frac{1}{3}}) = \frac{2}{3 ( 2 x + 7 ) ^{\frac{2}{3}}}

= 1 \cdot (2 x + 7)^{\frac{1}{3}} + \frac{2}{3 ( 2 x + 7 ) ^{\frac{2}{3}}} x

Vereinfache

1 \cdot (2 x + 7)^{\frac{1}{3}} + \frac{2}{3 ( 2 x + 7 ) ^{\frac{2}{3}}} x : \frac{8 x + 21}{3 ( 2 x + 7 ) ^{\frac{2}{3}}}

= \frac{8 x + 21}{3 ( 2 x + 7 ) ^{\frac{2}{3}}}

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