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

Lösung

ableitung von

\frac{1}{x ^{2} - 1}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

x y^{^{'}} = y + 8 x^{2} sin (x), y (π) = 0

x^{2} \frac{d y}{d x} + 2 x y - y^{3} = 0

\frac{d}{d x} (\frac{10}{x ^{7}})

x \to 0 - lim (\frac{1}{3 x})