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Beliebt Rechnen >

derivative of 3/(sqrt(x^5))

Lösung

\frac{d}{d x} (\frac{3}{x ^{5}})

Lösung

- \frac{15}{2 x ^{\frac{7}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{x ^{5}})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

3 (- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4}) : - \frac{15}{2 x ^{\frac{7}{2}}}

= - \frac{15}{2 x ^{\frac{7}{2}}}

Graph

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