derivative of pi/((2x^5))

Lösung

\frac{d}{d x} (\frac{π}{( 2 x ) ^{5}})

- \frac{5 π}{32 x ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{π}{( 2 x ) ^{5}})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

= π \frac{d}{d x} ((2 x)^{- 5})

Wende die Kettenregel an:

- \frac{5}{( 2 x ) ^{6}} \frac{d}{d x} (2 x)

= - \frac{5}{( 2 x ) ^{6}} \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

= π (- \frac{5}{( 2 x ) ^{6}} \cdot 2)

Vereinfache

π (- \frac{5}{( 2 x ) ^{6}} \cdot 2) : - \frac{5 π}{32 x ^{6}}

= - \frac{5 π}{32 x ^{6}}

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