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Beliebt Rechnen >

derivative f(x)=x^2(3-x)^2

Lösung

ableitung von

f (x) = x^{2} (3 - x)^{2}

Lösung

4 x^{3} - 18 x^{2} + 18 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x (3 - x)^{2} + (- 2 (3 - x)) x^{2} : 4 x^{3} - 18 x^{2} + 18 x

= 4 x^{3} - 18 x^{2} + 18 x

Graph

Beliebte Beispiele

limit as x approaches-1 of |x|-3

x \to - 1 lim (∣ x ∣ - 3)

derivative of sqrt(x)ln(2x)

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

limit as x approaches 2+of x^2

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

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

integral of (2x)/(sqrt(2x+1))

\int \frac{2 x}{2 x + 1} d x