d/(dt)(1/(sqrt(t)))

Lösung

\frac{d}{d t} (\frac{1}{t})

- \frac{1}{2 t ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d t} (\frac{1}{t})

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

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

= - \frac{1}{2} t^{- \frac{1}{2} - 1}

Vereinfache

- \frac{1}{2} t^{- \frac{1}{2} - 1} : - \frac{1}{2 t ^{\frac{3}{2}}}

= - \frac{1}{2 t ^{\frac{3}{2}}}

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