derivative of (x^2^{-1})

Lösung

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

- \frac{2}{x ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{2}{x ^{3}}