derivative (6x^2-10x)e^x

解

導関数

(6 x^{2} - 10 x) e^{x}

6 e^{x} x^{2} + 2 e^{x} x - 10 e^{x}

解答ステップ

\frac{d}{d x} ((6 x^{2} - 10 x) e^{x})

積の法則を適用:

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

f = 6 x^{2} - 10 x, g = e^{x}

= \frac{d}{d x} (6 x^{2} - 10 x) e^{x} + \frac{d}{d x} (e^{x}) (6 x^{2} - 10 x)

\frac{d}{d x} (6 x^{2} - 10 x) = 12 x - 10

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

= (12 x - 10) e^{x} + e^{x} (6 x^{2} - 10 x)

簡素化

(12 x - 10) e^{x} + e^{x} (6 x^{2} - 10 x) : 6 e^{x} x^{2} + 2 e^{x} x - 10 e^{x}

= 6 e^{x} x^{2} + 2 e^{x} x - 10 e^{x}