derivative 8/(xsqrt(x^2-4))

Lösung

ableitung von

\frac{8}{x x ^{2} - 4}

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to \infty lim ((k)^{x})

x \to 1 lim (tan (x))

y^{^{'}} = \frac{( x ^{4} y ^{4} + 4 x ^{4} )}{y ^{3}}

y^{^{''}} - 3 y^{^{'}} - 4 y = - 8 e^{t} cos (2 t)

d er i v a t i v e f (x) = e^{x} sin (x) - 3 e^{x} cos (x)