derivative x^3e^x-3x^2e^x+6xe^x-6e^x

解答

导数

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

e^{x} x^{3}

求解步骤

\frac{d}{d x} (x^{3} e^{x} - 3 x^{2} e^{x} + 6 x e^{x} - 6 e^{x})

使用微分加减法定则:

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

= \frac{d}{d x} (x^{3} e^{x}) - \frac{d}{d x} (3 x^{2} e^{x}) + \frac{d}{d x} (6 x e^{x}) - \frac{d}{d x} (6 e^{x})

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

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

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

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

= 3 x^{2} e^{x} + e^{x} x^{3} - 3 (2 x e^{x} + e^{x} x^{2}) + 6 (e^{x} + e^{x} x) - 6 e^{x}

化简

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

= e^{x} x^{3}

\frac{\partial}{\partial x} (9 - 2 x + 4 y - x^{2} - 4 y^{2})

a re a f (x) = \frac{3}{x} + x, 5, 15

d er i v a t i v e \frac{1}{2 t - 1}

\int (1 - t) (7 + t^{2}) d t

x \to 1 + lim (2 - x)