derivative of 1/(sqrt(x^2-9))

Lösung

\frac{d}{d x} (\frac{1}{x ^{2} - 9})

- \frac{x}{( x ^{2} - 9 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{2} - 9})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{2} - 9)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x ^{2} - 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} - 9)

= - \frac{1}{2 ( x ^{2} - 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} - 9)

\frac{d}{d x} (x^{2} - 9) = 2 x

= - \frac{1}{2 ( x ^{2} - 9 ) ^{\frac{3}{2}}} \cdot 2 x

Vereinfache

- \frac{1}{2 ( x ^{2} - 9 ) ^{\frac{3}{2}}} \cdot 2 x : - \frac{x}{( x ^{2} - 9 ) ^{\frac{3}{2}}}

= - \frac{x}{( x ^{2} - 9 ) ^{\frac{3}{2}}}