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

Lösung

ableitung von

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

\frac{2 x ( - 6 x ^{4} + 4 x ^{2} + 1 )}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1}) = \frac{- 6 x ^{4} + 4 x ^{2} + 1}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{2}}

= 2 \cdot \frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1} \cdot \frac{- 6 x ^{4} + 4 x ^{2} + 1}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{2}}

Vereinfache

2 \cdot \frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1} \cdot \frac{- 6 x ^{4} + 4 x ^{2} + 1}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{2}} : \frac{2 x ( - 6 x ^{4} + 4 x ^{2} + 1 )}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{3}}

= \frac{2 x ( - 6 x ^{4} + 4 x ^{2} + 1 )}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{3}}

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