derivative of (8x^2-14xe^x)

解

\frac{d}{d x} ((8 x^{2} - 14 x) e^{x})

8 e^{x} x^{2} + 2 e^{x} x - 14 e^{x}

解答ステップ

\frac{d}{d x} ((8 x^{2} - 14 x) e^{x})

積の法則を適用:

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

f = 8 x^{2} - 14 x, g = e^{x}

= \frac{d}{d x} (8 x^{2} - 14 x) e^{x} + \frac{d}{d x} (e^{x}) (8 x^{2} - 14 x)

\frac{d}{d x} (8 x^{2} - 14 x) = 16 x - 14

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

= (16 x - 14) e^{x} + e^{x} (8 x^{2} - 14 x)

簡素化

(16 x - 14) e^{x} + e^{x} (8 x^{2} - 14 x) : 8 e^{x} x^{2} + 2 e^{x} x - 14 e^{x}

= 8 e^{x} x^{2} + 2 e^{x} x - 14 e^{x}