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Beliebt Rechnen >

derivative f(x)= 5/(2x)

Lösung

ableitung von

f (x) = \frac{5}{2 x}

Lösung

- \frac{5}{2 x ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Vereinfache

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

= - \frac{5}{2 x ^{2}}

Graph

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