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Beliebt Rechnen >

derivative of x^2e^{5x}

Lösung

\frac{d}{d x} (x^{2} e^{5 x})

Lösung

2 x e^{5 x} + e^{5 x} \cdot 5 x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} e^{5 x})

Wende die Produktregel an:

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

f = x^{2}, g = e^{5 x}

= \frac{d}{d x} (x^{2}) e^{5 x} + \frac{d}{d x} (e^{5 x}) x^{2}

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

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= 2 x e^{5 x} + e^{5 x} \cdot 5 x^{2}

Graph

Beliebte Beispiele

derivative sqrt(7+4x)

d er i v a t i v e 7 + 4 x

integral from 0 to 4 of-x^2

\int_{0}^{4} - x^{2} d x

limit as x approaches 2 of 4-2x

x \to 2 lim (4 - 2 x)

(dy)/(dx)-y=3e^x+12e^{4x}

\frac{d y}{d x} - y = 3 e^{x} + 12 e^{4 x}

integral of x^2*sqrt(16-x^2)

\int x^{2} \cdot 16 - x^{2} d x