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Beliebt Rechnen >

derivative of 4/(sqrt(x+7))

Lösung

\frac{d}{d x} (\frac{4}{x + 7})

Lösung

- \frac{2}{x ( x + 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{x + 7})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (\frac{1}{x + 7})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

= 4 (- \frac{1}{( x + 7 ) ^{2}} \cdot \frac{1}{2 x})

Vereinfache

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

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

Graph

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