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Beliebt Rechnen >

derivative f(x)=x^2(x+1)

Lösung

ableitung von

f (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

derivative f(x)=(2x^2)/(x^2-2x-8)

d er i v a t i v e f (x) = \frac{2 x ^{2}}{x ^{2} - 2 x - 8}

integral of x/(x^2+2x)

\int \frac{x}{x ^{2} + 2 x} d x

derivative ((t^3)/(t^8+1))^2

d er i v a t i v e (\frac{t ^{3}}{t ^{8} + 1})^{2}

y^{''}+4y=cos(t)

y^{^{''}} + 4 y = cos (t)

derivative \sqrt[7]{x^6}-x^{sqrt(2)}

d er i v a t i v e 7 x^{6} - x^{2}