derivative of (θ(e^θ)(2θ))

解

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

2 (e^{x} x^{2} + 2 x e^{x})

解答ステップ

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

簡素化

(x) (e^{x}) (2 x) : 2 e^{x} x^{2}

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

定数を除去:

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

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

積の法則を適用:

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

f = e^{x}, g = x^{2}

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

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

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

= 2 (e^{x} x^{2} + 2 x e^{x})