derivative 3x^2e^x+e^x(x^3+2)

解答

导数

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

e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 2 e^{x}

求解步骤

\frac{d}{d x} (3 x^{2} e^{x} + e^{x} (x^{3} + 2))

使用微分加减法定则:

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

= \frac{d}{d x} (3 x^{2} e^{x}) + \frac{d}{d x} (e^{x} (x^{3} + 2))

\frac{d}{d x} (3 x^{2} e^{x}) = 3 (2 x e^{x} + e^{x} x^{2})

\frac{d}{d x} (e^{x} (x^{3} + 2)) = e^{x} (x^{3} + 2) + 3 x^{2} e^{x}

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

化简

3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 2) + 3 x^{2} e^{x} : e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 2 e^{x}

= e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 2 e^{x}

\frac{d}{d x} (x \frac{1}{2})

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