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Beliebt Rechnen >

derivative of (3x^4(4x^3+4x))

Lösung

\frac{d}{d x} ((3 x^{4}) (4 x^{3} + 4 x))

Lösung

3 (28 x^{6} + 20 x^{4})

Schritte zur Lösung

\frac{d}{d x} ((3 x^{4}) (4 x^{3} + 4 x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x^{4} (4 x^{3} + 4 x))

Wende die Produktregel an:

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

f = x^{4}, g = 4 x^{3} + 4 x

= 3 (\frac{d}{d x} (x^{4}) (4 x^{3} + 4 x) + \frac{d}{d x} (4 x^{3} + 4 x) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (4 x^{3} + 4 x) = 12 x^{2} + 4

= 3 (4 x^{3} (4 x^{3} + 4 x) + (12 x^{2} + 4) x^{4})

Multipliziere aus

4 x^{3} (4 x^{3} + 4 x) + (12 x^{2} + 4) x^{4} : 28 x^{6} + 20 x^{4}

= 3 (28 x^{6} + 20 x^{4})

Graph

Beliebte Beispiele

derivative f(x)=(7x^2-12x)e^x

d er i v a t i v e f (x) = (7 x^{2} - 12 x) e^{x}

fläche 3x^2,x^2+6

a re a 3 x^{2}, x^{2} + 6

\frac{d y}{d x} = 6 x y

derivative 2e^x

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

integral from 0 to 1 of 2+sqrt(2+x^2)

\int_{0}^{1} 2 + 2 + x^{2} d x