derivative of-e^x(x+6)

解

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

- e^{x} x - 7 e^{x}

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

積の法則を適用:

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

f = e^{x}, g = x + 6

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

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

\frac{d}{d x} (x + 6) = 1

= - (e^{x} (x + 6) + 1 \cdot e^{x})

簡素化

- (e^{x} (x + 6) + 1 \cdot e^{x}) : - e^{x} x - 7 e^{x}

= - e^{x} x - 7 e^{x}