derivative of 1/(sqrt(10x+11))

Lösung

\frac{d}{d x} (\frac{1}{10 x + 11})

- \frac{5}{( 10 x + 11 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{10 x + 11})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((10 x + 11)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 10 x + 11 ) ^{\frac{3}{2}}} \frac{d}{d x} (10 x + 11)

= - \frac{1}{2 ( 10 x + 11 ) ^{\frac{3}{2}}} \frac{d}{d x} (10 x + 11)

\frac{d}{d x} (10 x + 11) = 10

= - \frac{1}{2 ( 10 x + 11 ) ^{\frac{3}{2}}} \cdot 10

Vereinfache

- \frac{1}{2 ( 10 x + 11 ) ^{\frac{3}{2}}} \cdot 10 : - \frac{5}{( 10 x + 11 ) ^{\frac{3}{2}}}

= - \frac{5}{( 10 x + 11 ) ^{\frac{3}{2}}}

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