derivative h(x)=(x+x^{-1})^3

Lösung

ableitung von

h (x) = (x + x^{- 1})^{3}

3 x^{2} - \frac{3}{x ^{2}} - \frac{3}{x ^{4}} + 3

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= 3 x^{2} - \frac{3}{x ^{2}} - \frac{3}{x ^{4}} + 3

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