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Beliebt Rechnen >

derivative y=(x^3+8)e^x

Lösung

ableitung von

y = (x^{3} + 8) e^{x}

Lösung

3 x^{2} e^{x} + e^{x} (x^{3} + 8)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 8) e^{x})

Wende die Produktregel an:

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

f = x^{3} + 8, g = e^{x}

= \frac{d}{d x} (x^{3} + 8) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 8)

\frac{d}{d x} (x^{3} + 8) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 8)

Graph

Beliebte Beispiele

integral of (x^3+4)^4(3x^2)

\int (x^{3} + 4)^{4} (3 x^{2}) d x

derivative of sqrt(x\sqrt{x)}

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

\int 3 d x

limit as x approaches 0-of e^{8/x}

x \to 0 - lim (e^{\frac{8}{x}})

integral of cot^5(6x)

\int cot^{5} (6 x) d x