derivative f(x)=(4x^2-8x+8)e^x

解答

导数

f (x) = (4 x^{2} - 8 x + 8) e^{x}

4 e^{x} x^{2}

求解步骤

\frac{d}{d x} ((4 x^{2} - 8 x + 8) e^{x})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4 x^{2} - 8 x + 8, g = e^{x}

= \frac{d}{d x} (4 x^{2} - 8 x + 8) e^{x} + \frac{d}{d x} (e^{x}) (4 x^{2} - 8 x + 8)

\frac{d}{d x} (4 x^{2} - 8 x + 8) = 8 x - 8

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

= (8 x - 8) e^{x} + e^{x} (4 x^{2} - 8 x + 8)

化简

(8 x - 8) e^{x} + e^{x} (4 x^{2} - 8 x + 8) : 4 e^{x} x^{2}

= 4 e^{x} x^{2}

\frac{\partial}{\partial y} (x e^{2 y} sin (7 z))

\int_{- 8}^{64} \frac{1}{3 x} d x

d er i v a t i v e 24 x - 0.01 x^{2}

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x \to 0 - lim (\frac{1 - e ^{- 3 x}}{x})