derivative of e^x(x+6)

Lösung

\frac{d}{d x} (e^{x} (x + 6))

e^{x} x + 7 e^{x}

Schritte zur Lösung

\frac{d}{d x} (e^{x} (x + 6))

Wende die Produktregel an:

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

f = e^{x}, g = x + 6

= \frac{d}{d x} (e^{x}) (x + 6) + \frac{d}{d x} (x + 6) e^{x}

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

\frac{d}{d x} (x + 6) = 1

= e^{x} (x + 6) + 1 \cdot e^{x}

Vereinfache

e^{x} (x + 6) + 1 \cdot e^{x} : e^{x} x + 7 e^{x}

= e^{x} x + 7 e^{x}

x \to - 9 lim (\frac{9 - ∣ x ∣}{9 + x})

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