derivative of e^x(8x^2-16x+16)

解

\frac{d}{d x} (e^{x} (8 x^{2} - 16 x + 16))

8 e^{x} x^{2}

解答ステップ

\frac{d}{d x} (e^{x} (8 x^{2} - 16 x + 16))

積の法則を適用:

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

f = e^{x}, g = 8 x^{2} - 16 x + 16

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

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

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

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

簡素化

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

= 8 e^{x} x^{2}