derivative of e^xx^2+4e^xx+2e^x

解答

\frac{d}{d x} (e^{x} x^{2} + 4 e^{x} x + 2 e^{x})

e^{x} x^{2} + 6 e^{x} x + 6 e^{x}

求解步骤

\frac{d}{d x} (e^{x} x^{2} + 4 e^{x} x + 2 e^{x})

使用微分加减法定则:

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

= \frac{d}{d x} (e^{x} x^{2}) + \frac{d}{d x} (4 e^{x} x) + \frac{d}{d x} (2 e^{x})

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

\frac{d}{d x} (4 e^{x} x) = 4 (e^{x} x + e^{x})

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

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

化简

e^{x} x^{2} + 2 x e^{x} + 4 (e^{x} x + e^{x}) + 2 e^{x} : e^{x} x^{2} + 6 e^{x} x + 6 e^{x}

= e^{x} x^{2} + 6 e^{x} x + 6 e^{x}

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