derivative of 3/(sqrt(x+1))

Lösung

\frac{d}{d x} (\frac{3}{x + 1})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{x + 1})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{1}{x + 1})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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