derivative of 2/(\sqrt[4]{x^3})

Lösung

\frac{d}{d x} (\frac{2}{4 x ^{3}})

- \frac{3}{2 x ^{\frac{7}{4}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{4 x ^{3}})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (\frac{1}{4 x ^{3}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 2 \frac{d}{d x} ((x^{3})^{- \frac{1}{4}})

Wende die Kettenregel an:

- \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \frac{d}{d x} (x^{3})

= - \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \frac{d}{d x} (x^{3})

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

= 2 (- \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \cdot 3 x^{2})

Vereinfache

2 (- \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \cdot 3 x^{2}) : - \frac{3}{2 x ^{\frac{7}{4}}}

= - \frac{3}{2 x ^{\frac{7}{4}}}

x \frac{d y}{d x} = e^{y + x}

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