derivative of 1/(2sqrt(x+4))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e ln (\frac{4 x + 1}{x ^{2} - 1})

\int_{0}^{5} \frac{w}{w - 2} d w

x \to 0 lim (3 x cos (x))

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

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