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Beliebt Rechnen >

derivative of x^2(x+1)

Lösung

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

Lösung

3 x^{2} + 2 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = x + 1

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

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

\frac{d}{d x} (x + 1) = 1

= 2 x (x + 1) + 1 \cdot x^{2}

Vereinfache

2 x (x + 1) + 1 \cdot x^{2} : 3 x^{2} + 2 x

= 3 x^{2} + 2 x

Graph

Beliebte Beispiele

(d^2)/(dx^2)(sqrt(x)ln(x))

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

derivative-(0.1x-23)^2

d er i v a t i v e - (0.1 x - 23)^{2}

integral of 2e^{-3t}

\int 2 e^{- 3 t} d t

derivative sqrt(\sqrt{4x+3)}

d er i v a t i v e 4 x + 3

slopeintercept (-4,2),(6,-3)

s l o p e in t erce pt (- 4, 2), (6, - 3)