derivative of 2xe^y

解

\frac{d}{d x} (2 x e^{y})

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

解答ステップ

\frac{d}{d x} (2 x e^{y})

定数を除去:

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

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

積の法則を適用:

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

f = x, g = e^{y}

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

\frac{d x}{d x} = 1

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

= 2 (1 \cdot e^{y} + e^{y} \frac{d y}{d x} x)

簡素化

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