derivative (4-1/(2x^2))^{-1}

Lösung

ableitung von

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

- \frac{4 x}{( 8 x ^{2} - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} ((4 - \frac{1}{2 x ^{2}})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 4 - \frac{1}{2 x ^{2}} ) ^{2}} \frac{d}{d x} (4 - \frac{1}{2 x ^{2}})

= - \frac{1}{( 4 - \frac{1}{2 x ^{2}} ) ^{2}} \frac{d}{d x} (4 - \frac{1}{2 x ^{2}})

\frac{d}{d x} (4 - \frac{1}{2 x ^{2}}) = \frac{1}{x ^{3}}

= - \frac{1}{( 4 - \frac{1}{2 x ^{2}} ) ^{2}} \cdot \frac{1}{x ^{3}}

Vereinfache

- \frac{1}{( 4 - \frac{1}{2 x ^{2}} ) ^{2}} \cdot \frac{1}{x ^{3}} : - \frac{4 x}{( 8 x ^{2} - 1 ) ^{2}}

= - \frac{4 x}{( 8 x ^{2} - 1 ) ^{2}}

\frac{\partial}{\partial x} (\frac{x - 3 y}{x ^{2} + y ^{2}})

\frac{d}{d x} (arctan (\frac{x}{1 + x}))

\int \frac{( 4 x ^{3} - 3 x ^{2} - 8 x )}{6 x} d x

x \to 0 lim (x^{2} sin (\frac{1}{x}))

\frac{d}{d x} ((5 x^{6} + 2 x^{3})^{4})