derivative of (7x^2-11xe^x)

解

\frac{d}{d x} ((7 x^{2} - 11 x) e^{x})

7 e^{x} x^{2} + 3 e^{x} x - 11 e^{x}

解答ステップ

\frac{d}{d x} ((7 x^{2} - 11 x) e^{x})

積の法則を適用:

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

f = 7 x^{2} - 11 x, g = e^{x}

= \frac{d}{d x} (7 x^{2} - 11 x) e^{x} + \frac{d}{d x} (e^{x}) (7 x^{2} - 11 x)

\frac{d}{d x} (7 x^{2} - 11 x) = 14 x - 11

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

= (14 x - 11) e^{x} + e^{x} (7 x^{2} - 11 x)

簡素化

(14 x - 11) e^{x} + e^{x} (7 x^{2} - 11 x) : 7 e^{x} x^{2} + 3 e^{x} x - 11 e^{x}

= 7 e^{x} x^{2} + 3 e^{x} x - 11 e^{x}