derivative of 6x^2e^x

解

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

6 (2 x e^{x} + e^{x} x^{2})

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

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

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

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

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

= 6 (2 x e^{x} + e^{x} x^{2})