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Beliebt Rechnen >

derivative of 3/(sqrt(7x^4-5x^2+1))

Lösung

\frac{d}{d x} (\frac{3}{7 x ^{4} - 5 x ^{2} + 1})

Lösung

- \frac{3 x ( 14 x ^{2} - 5 )}{( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{7 x ^{4} - 5 x ^{2} + 1})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{1}{7 x ^{4} - 5 x ^{2} + 1})

Wende Exponentenregel an:

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

= 3 \frac{d}{d x} ((7 x^{4} - 5 x^{2} + 1)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x^{4} - 5 x^{2} + 1)

= - \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x^{4} - 5 x^{2} + 1)

\frac{d}{d x} (7 x^{4} - 5 x^{2} + 1) = 28 x^{3} - 10 x

= 3 (- \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} (28 x^{3} - 10 x))

Vereinfache

3 (- \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} (28 x^{3} - 10 x)) : - \frac{3 x ( 14 x ^{2} - 5 )}{( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

= - \frac{3 x ( 14 x ^{2} - 5 )}{( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

Graph

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