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Beliebt Rechnen >

derivative of 9x^9e^{x-1}

Lösung

\frac{d}{d x} (9 x^{9} e^{x - 1})

Lösung

9 (9 x^{8} e^{x - 1} + e^{x - 1} x^{9})

Schritte zur Lösung

\frac{d}{d x} (9 x^{9} e^{x - 1})

Entferne die Konstante:

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

= 9 \frac{d}{d x} (x^{9} e^{x - 1})

Wende die Produktregel an:

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

f = x^{9}, g = e^{x - 1}

= 9 (\frac{d}{d x} (x^{9}) e^{x - 1} + \frac{d}{d x} (e^{x - 1}) x^{9})

\frac{d}{d x} (x^{9}) = 9 x^{8}

\frac{d}{d x} (e^{x - 1}) = e^{x - 1}

= 9 (9 x^{8} e^{x - 1} + e^{x - 1} x^{9})

Graph

Beliebte Beispiele

integral of 5/(xln(3x))

\int \frac{5}{x ln ( 3 x )} d x

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x \to 6 - lim (7 - x)

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\int \frac{1}{x ^{- 3}} d x

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