derivative of (x+3e^{6x})

Lösung

\frac{d}{d x} ((x + 3) e^{6 x})

6 e^{6 x} x + 19 e^{6 x}

Schritte zur Lösung

\frac{d}{d x} ((x + 3) e^{6 x})

Wende die Produktregel an:

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

f = x + 3, g = e^{6 x}

= \frac{d}{d x} (x + 3) e^{6 x} + \frac{d}{d x} (e^{6 x}) (x + 3)

\frac{d}{d x} (x + 3) = 1

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

= 1 \cdot e^{6 x} + e^{6 x} \cdot 6 (x + 3)

Vereinfache

1 \cdot e^{6 x} + e^{6 x} \cdot 6 (x + 3) : 6 e^{6 x} x + 19 e^{6 x}

= 6 e^{6 x} x + 19 e^{6 x}

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\frac{\partial}{\partial x} (x e^{x y} - 2 y)