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Beliebt Rechnen >

derivative f(x)= 1/(sqrt(x-4))

Lösung

ableitung von

f (x) = \frac{1}{x - 4}

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x - 4})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x - 4) = 1

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

Vereinfache

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

Graph

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