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Beliebt Rechnen >

derivative x(3x+4)^5

Lösung

ableitung von

x (3 x + 4)^{5}

Lösung

(3 x + 4)^{5} + 15 x (3 x + 4)^{4}

Schritte zur Lösung

\frac{d}{d x} (x (3 x + 4)^{5})

Wende die Produktregel an:

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

f = x, g = (3 x + 4)^{5}

= \frac{d x}{d x} (3 x + 4)^{5} + \frac{d}{d x} ((3 x + 4)^{5}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((3 x + 4)^{5}) = 15 (3 x + 4)^{4}

= 1 \cdot (3 x + 4)^{5} + 15 (3 x + 4)^{4} x

Vereinfache

= (3 x + 4)^{5} + 15 x (3 x + 4)^{4}

Graph

Beliebte Beispiele

y=(x^2-2x+2)e^x

y = (x^{2} - 2 x + 2) e^{x}

derivative (x^3+1)^5

d er i v a t i v e (x^{3} + 1)^{5}

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\int 4 x^{3} + 9 x^{2} y^{2} + 3 d x

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integral of (1.3)^x

\int (1.3)^{x} d x