derivative of 44(2x^3-5^{6/5})

Lösung

\frac{d}{d x} (44 (2 x^{3} - 5)^{\frac{6}{5}})

\frac{1584 x ^{2} ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5}

Schritte zur Lösung

\frac{d}{d x} (44 (2 x^{3} - 5)^{\frac{6}{5}})

Entferne die Konstante:

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

= 44 \frac{d}{d x} ((2 x^{3} - 5)^{\frac{6}{5}})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x^{3} - 5) = 6 x^{2}

= 44 \cdot \frac{6 ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5} \cdot 6 x^{2}

Vereinfache

44 \cdot \frac{6 ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5} \cdot 6 x^{2} : \frac{1584 x ^{2} ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5}

= \frac{1584 x ^{2} ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5}

\frac{d}{d x} (x^{3} os (x))

n = 7 \sum \infty \frac{n ^{2}}{e ^{n}}

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

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