derivative (5x^2-10x+10)e^x

解

導関数

(5 x^{2} - 10 x + 10) e^{x}

5 e^{x} x^{2}

解答ステップ

\frac{d}{d x} ((5 x^{2} - 10 x + 10) e^{x})

積の法則を適用:

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

f = 5 x^{2} - 10 x + 10, g = e^{x}

= \frac{d}{d x} (5 x^{2} - 10 x + 10) e^{x} + \frac{d}{d x} (e^{x}) (5 x^{2} - 10 x + 10)

\frac{d}{d x} (5 x^{2} - 10 x + 10) = 10 x - 10

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

= (10 x - 10) e^{x} + e^{x} (5 x^{2} - 10 x + 10)

簡素化

(10 x - 10) e^{x} + e^{x} (5 x^{2} - 10 x + 10) : 5 e^{x} x^{2}

= 5 e^{x} x^{2}