derivative of 1/(2(1-x^{3/2)})

Lösung

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

\frac{3}{4 ( 1 - x ) ^{\frac{5}{2}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{3}{2 ( 1 - x ) ^{\frac{5}{2}}} \frac{d}{d x} (1 - x)

= - \frac{3}{2 ( 1 - x ) ^{\frac{5}{2}}} \frac{d}{d x} (1 - x)

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

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

Vereinfache

\frac{1}{2} (- \frac{3}{2 ( 1 - x ) ^{\frac{5}{2}}} (- 1)) : \frac{3}{4 ( 1 - x ) ^{\frac{5}{2}}}

= \frac{3}{4 ( 1 - x ) ^{\frac{5}{2}}}

f (x) = sinh^{2} (x)

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