derivative of (4x^2-8x+8e^x)

解

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

4 e^{x} x^{2}

解答ステップ

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

積の法則を適用:

(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)

簡素化

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

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