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

解

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

e^{x} x^{2}

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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

= e^{x} x^{2}