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Beliebt Rechnen >

derivative of 2x^2sqrt(2-x)

Lösung

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

Lösung

\frac{- 5 x ^{2} + 8 x}{2 - x}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 (2 x 2 - x + (- \frac{1}{2 2 - x}) x^{2}) : \frac{- 5 x ^{2} + 8 x}{2 - x}

= \frac{- 5 x ^{2} + 8 x}{2 - x}

Graph

Beliebte Beispiele

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