derivative of 9(2xe^x+e^xx^2)

解答

\frac{d}{d x} (9 (2 x e^{x} + e^{x} x^{2}))

9 (e^{x} x^{2} + 4 e^{x} x + 2 e^{x})

求解步骤

\frac{d}{d x} (9 (2 x e^{x} + e^{x} x^{2}))

将常数提出:

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

= 9 \frac{d}{d x} (2 x e^{x} + e^{x} x^{2})

使用微分加减法定则:

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

= 9 (\frac{d}{d x} (2 x e^{x}) + \frac{d}{d x} (e^{x} x^{2}))

\frac{d}{d x} (2 x e^{x}) = 2 (e^{x} + e^{x} x)

\frac{d}{d x} (e^{x} x^{2}) = e^{x} x^{2} + 2 x e^{x}

= 9 (2 (e^{x} + e^{x} x) + e^{x} x^{2} + 2 x e^{x})

乘开

2 (e^{x} + e^{x} x) + e^{x} x^{2} + 2 x e^{x} : e^{x} x^{2} + 4 e^{x} x + 2 e^{x}

= 9 (e^{x} x^{2} + 4 e^{x} x + 2 e^{x})

\int_{1}^{4} \frac{5}{x} d x

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