derivative of x^7e^{9x}

Lösung

\frac{d}{d x} (x^{7} e^{9 x})

7 x^{6} e^{9 x} + e^{9 x} \cdot 9 x^{7}

Schritte zur Lösung

\frac{d}{d x} (x^{7} e^{9 x})

Wende die Produktregel an:

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

f = x^{7}, g = e^{9 x}

= \frac{d}{d x} (x^{7}) e^{9 x} + \frac{d}{d x} (e^{9 x}) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 7 x^{6} e^{9 x} + e^{9 x} \cdot 9 x^{7}

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