derivative of 3(e^x+xe^x)

解答

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

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

求解步骤

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

将常数提出:

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

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

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

化简

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

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