derivative of x^2sqrt(3-x)

Lösung

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

\frac{- 5 x ^{2} + 12 x}{2 3 - x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x 3 - x + (- \frac{1}{2 3 - x}) x^{2} : \frac{- 5 x ^{2} + 12 x}{2 3 - x}

= \frac{- 5 x ^{2} + 12 x}{2 3 - x}

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