derivative (x^2)^{-1}

Lösung

ableitung von

(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}}

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

\int \frac{1}{x ( 10 - x )} d x

\frac{\partial}{\partial x} (\frac{x + 2}{y + 1})

\frac{d}{d x} (x e^{9 x})

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 9)