derivative of 5/(sqrt(x+8))

Lösung

\frac{d}{d x} (\frac{5}{x + 8})

- \frac{5}{2 ( x + 8 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{x + 8})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (\frac{1}{x + 8})

Wende Exponentenregel an:

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

= 5 \frac{d}{d x} ((x + 8)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

= - \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

\frac{d}{d x} (x + 8) = 1

= 5 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1)

Vereinfache

5 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{5}{2 ( x + 8 ) ^{\frac{3}{2}}}

= - \frac{5}{2 ( x + 8 ) ^{\frac{3}{2}}}

\frac{d}{d x} (ln (4 sin^{2} (x)))

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n = 2 \sum \infty \frac{7}{2 ^{n}}