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Beliebt Rechnen >

derivative of 4xe^{5x}

Lösung

\frac{d}{d x} (4 x e^{5 x})

Lösung

4 (e^{5 x} + 5 e^{5 x} x)

Schritte zur Lösung

\frac{d}{d x} (4 x e^{5 x})

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

= 4 (e^{5 x} + 5 e^{5 x} x)

Graph

Beliebte Beispiele

integral of (x^2)/((5-x^3)^2)

\int \frac{x ^{2}}{( 5 - x ^{3} ) ^{2}} d x

integral of e^{5x}(5)

\int e^{5 x} (5) d x

integral from 0 to 1 of (e^{sqrt(x)})^2

\int_{0}^{1} (e^{x})^{2} d x

limit as x approaches infinity of x^3-3x

x \to \infty lim (x^{3} - 3 x)

derivative of (2x^2-1^2)

\frac{d}{d x} ((2 x^{2} - 1)^{2})