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Beliebt Rechnen >

derivative 3/(sqrt(6t+3))

Lösung

ableitung von

\frac{3}{6 t + 3}

Lösung

- \frac{9}{( 6 t + 3 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d t} (\frac{3}{6 t + 3})

Entferne die Konstante:

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

= 3 \frac{d}{d t} (\frac{1}{6 t + 3})

Wende Exponentenregel an:

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

= 3 \frac{d}{d t} ((6 t + 3)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 6 t + 3 ) ^{\frac{3}{2}}} \frac{d}{d t} (6 t + 3)

= - \frac{1}{2 ( 6 t + 3 ) ^{\frac{3}{2}}} \frac{d}{d t} (6 t + 3)

\frac{d}{d t} (6 t + 3) = 6

= 3 (- \frac{1}{2 ( 6 t + 3 ) ^{\frac{3}{2}}} \cdot 6)

Vereinfache

3 (- \frac{1}{2 ( 6 t + 3 ) ^{\frac{3}{2}}} \cdot 6) : - \frac{9}{( 6 t + 3 ) ^{\frac{3}{2}}}

= - \frac{9}{( 6 t + 3 ) ^{\frac{3}{2}}}

Graph

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