derivative y=(x+2/x)(7-2x^3)

Lösung

ableitung von

y = (x + \frac{2}{x}) (7 - 2 x^{3})

- 8 x^{3} - 8 x - \frac{14}{x ^{2}} + 7

Schritte zur Lösung

\frac{d}{d x} ((x + \frac{2}{x}) (7 - 2 x^{3}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + \frac{2}{x}, g = 7 - 2 x^{3}

= \frac{d}{d x} (x + \frac{2}{x}) (7 - 2 x^{3}) + \frac{d}{d x} (7 - 2 x^{3}) (x + \frac{2}{x})

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

\frac{d}{d x} (7 - 2 x^{3}) = - 6 x^{2}

= (1 - \frac{2}{x ^{2}}) (7 - 2 x^{3}) + (- 6 x^{2}) (x + \frac{2}{x})

Vereinfache

(1 - \frac{2}{x ^{2}}) (7 - 2 x^{3}) + (- 6 x^{2}) (x + \frac{2}{x}) : - 8 x^{3} - 8 x - \frac{14}{x ^{2}} + 7

= - 8 x^{3} - 8 x - \frac{14}{x ^{2}} + 7

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