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Beliebt Rechnen >

derivative of 1/(sqrt(7x))

Lösung

\frac{d}{d x} (\frac{1}{7 x})

Lösung

- \frac{1}{2 7 x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{7 x})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((7 x)^{- \frac{1}{2}})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (7 x) = 7

= - \frac{1}{2 ( 7 x ) ^{\frac{3}{2}}} \cdot 7

Vereinfache

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

= - \frac{1}{2 7 x ^{\frac{3}{2}}}

Graph

Beliebte Beispiele

integral of (x^2-1)(sqrt(2x+1))

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

integral of cos^6(2x)

\int cos^{6} (2 x) d x

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\frac{d y}{d x} = e^{2 y + 8 x}

derivative of sin^3(x^2+7)

\frac{d}{d x} (sin^{3} (x^{2} + 7))