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Beliebt Rechnen >

derivative f(x)=x^2(2+x^{-3})

Lösung

ableitung von

f (x) = x^{2} (2 + x^{- 3})

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= 4 x - \frac{1}{x ^{2}}

Graph

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