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Beliebt Rechnen >

derivative (10\sqrt[3]{z})/(z^2)

Lösung

ableitung von

\frac{10 3 z}{z ^{2}}

Lösung

- \frac{50}{3 z ^{\frac{8}{3}}}

Schritte zur Lösung

\frac{d}{d z} (\frac{10 3 z}{z ^{2}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d z} (\frac{3 z}{z ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 10 \cdot \frac{\frac{d}{d z} ( 3 z ) z ^{2} - \frac{d}{d z} ( z ^{2} ) 3 z}{( z ^{2} ) ^{2}}

\frac{d}{d z} (3 z) = \frac{1}{3 z ^{\frac{2}{3}}}

\frac{d}{d z} (z^{2}) = 2 z

= 10 \cdot \frac{\frac{1}{3 z ^{\frac{2}{3}}} z ^{2} - 2 z 3 z}{( z ^{2} ) ^{2}}

Vereinfache

10 \cdot \frac{\frac{1}{3 z ^{\frac{2}{3}}} z ^{2} - 2 z 3 z}{( z ^{2} ) ^{2}} : - \frac{50}{3 z ^{\frac{8}{3}}}

= - \frac{50}{3 z ^{\frac{8}{3}}}

Graph

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