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Beliebt Rechnen >

derivative y=47(2t^3-9)^{6/5}

Lösung

ableitung von

y = 47 (2 t^{3} - 9)^{\frac{6}{5}}

Lösung

\frac{1692 t ^{2} ( 2 t ^{3} - 9 ) ^{\frac{1}{5}}}{5}

Schritte zur Lösung

\frac{d}{d t} (47 (2 t^{3} - 9)^{\frac{6}{5}})

Entferne die Konstante:

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

= 47 \frac{d}{d t} ((2 t^{3} - 9)^{\frac{6}{5}})

Wende die Kettenregel an:

\frac{6 ( 2 t ^{3} - 9 ) ^{\frac{1}{5}}}{5} \frac{d}{d t} (2 t^{3} - 9)

= \frac{6 ( 2 t ^{3} - 9 ) ^{\frac{1}{5}}}{5} \frac{d}{d t} (2 t^{3} - 9)

\frac{d}{d t} (2 t^{3} - 9) = 6 t^{2}

= 47 \cdot \frac{6 ( 2 t ^{3} - 9 ) ^{\frac{1}{5}}}{5} \cdot 6 t^{2}

Vereinfache

47 \cdot \frac{6 ( 2 t ^{3} - 9 ) ^{\frac{1}{5}}}{5} \cdot 6 t^{2} : \frac{1692 t ^{2} ( 2 t ^{3} - 9 ) ^{\frac{1}{5}}}{5}

= \frac{1692 t ^{2} ( 2 t ^{3} - 9 ) ^{\frac{1}{5}}}{5}

Graph

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