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Beliebt Rechnen >

derivative x^2(3-x)

Lösung

ableitung von

x^{2} (3 - x)

Lösung

6 x - 3 x^{2}

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) = - 1

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

Vereinfache

2 x (3 - x) + (- 1) x^{2} : 6 x - 3 x^{2}

= 6 x - 3 x^{2}

Graph

Beliebte Beispiele

derivative cy^{-6}

d er i v a t i v e c y^{- 6}

limit as x approaches 1 of x^3-2x^2+x-3

x \to 1 lim (x^{3} - 2 x^{2} + x - 3)

d er i v a t i v e x^{6}

derivative of (90/x)

\frac{d}{d x} (\frac{90}{x})

limit as x approaches infinity of x^2+1

x \to \infty lim (x^{2} + 1)