derivative of (24/(x^2+4x))

Lösung

\frac{d}{d x} (\frac{24}{x ^{2} + 4 x})

- \frac{24 ( 2 x + 4 )}{( x ^{2} + 4 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{24}{x ^{2} + 4 x})

Entferne die Konstante:

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

= 24 \frac{d}{d x} (\frac{1}{x ^{2} + 4 x})

Wende Exponentenregel an:

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

= 24 \frac{d}{d x} ((x^{2} + 4 x)^{- 1})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{2} + 4 x) = 2 x + 4

= 24 (- \frac{1}{( x ^{2} + 4 x ) ^{2}} (2 x + 4))

Vereinfache

24 (- \frac{1}{( x ^{2} + 4 x ) ^{2}} (2 x + 4)) : - \frac{24 ( 2 x + 4 )}{( x ^{2} + 4 x ) ^{2}}

= - \frac{24 ( 2 x + 4 )}{( x ^{2} + 4 x ) ^{2}}

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