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Beliebt Rechnen >

derivative of 3/(sqrt(16+x^4))

Lösung

\frac{d}{d x} (\frac{3}{16 + x ^{4}})

Lösung

- \frac{6 x ^{3}}{( 16 + x ^{4} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{16 + x ^{4}})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{1}{16 + x ^{4}})

Wende Exponentenregel an:

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

= 3 \frac{d}{d x} ((16 + x^{4})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 16 + x ^{4} ) ^{\frac{3}{2}}} \frac{d}{d x} (16 + x^{4})

= - \frac{1}{2 ( 16 + x ^{4} ) ^{\frac{3}{2}}} \frac{d}{d x} (16 + x^{4})

\frac{d}{d x} (16 + x^{4}) = 4 x^{3}

= 3 (- \frac{1}{2 ( 16 + x ^{4} ) ^{\frac{3}{2}}} \cdot 4 x^{3})

Vereinfache

3 (- \frac{1}{2 ( 16 + x ^{4} ) ^{\frac{3}{2}}} \cdot 4 x^{3}) : - \frac{6 x ^{3}}{( 16 + x ^{4} ) ^{\frac{3}{2}}}

= - \frac{6 x ^{3}}{( 16 + x ^{4} ) ^{\frac{3}{2}}}

Graph

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