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Beliebt Rechnen >

((x+30)\sqrt[3]{2-x})^'

Lösung

((x + 30) 3 2 - x)^{^{'}}

Lösung

3 2 - x - \frac{x + 30}{3 ( 2 - x ) ^{\frac{2}{3}}}

Schritte zur Lösung

((x + 30) 3 2 - x)^{'}

Wende die Produktregel an:

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

f = x + 30, g = 3 2 - x

= (x + 30)^{^{'}} 3 2 - x + (3 2 - x)^{^{'}} (x + 30)

(x + 30)^{'} = 1

(3 2 - x)^{'} = - \frac{1}{3 ( 2 - x ) ^{\frac{2}{3}}}

= 1 \cdot 3 2 - x + (- \frac{1}{3 ( 2 - x ) ^{\frac{2}{3}}}) (x + 30)

Vereinfache

1 \cdot 3 2 - x + (- \frac{1}{3 ( 2 - x ) ^{\frac{2}{3}}}) (x + 30) : 3 2 - x - \frac{x + 30}{3 ( 2 - x ) ^{\frac{2}{3}}}

= 3 2 - x - \frac{x + 30}{3 ( 2 - x ) ^{\frac{2}{3}}}

Graph

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